Elliptic curves over Q(14)\Q(\sqrt{14})

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
1.1-a1	1.1-a	$4$	$14$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	1.1	$1$	$1$	$0.66870$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓		✓	✓			$1$	$1$	$1$	$26.16385905$	0.874073183	$-3375$	$\bigl[a + 1$ , $a$ , $1$ , $2 a + 10$ , $2 a + 7\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(2a+10\right){x}+2a+7$
1.1-a2	1.1-a	$4$	$14$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	1.1	$1$	$1$	$0.66870$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓		✓	✓			$1$	$1$	$1$	$26.16385905$	0.874073183	$-3375$	$\bigl[a + 1$ , $a$ , $a + 1$ , $4 a + 3$ , $a + 21\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(4a+3\right){x}+a+21$
1.1-a3	1.1-a	$4$	$14$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	1.1	$1$	$1$	$0.66870$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-28$	$N(\mathrm{U}(1))$	✓		✓	✓			$1$	$1$	$1$	$26.16385905$	0.874073183	$16581375$	$\bigl[a + 1$ , $a$ , $1$ , $-18 a - 65$ , $41 a + 153\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-18a-65\right){x}+41a+153$
1.1-a4	1.1-a	$4$	$14$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	1.1	$1$	$1$	$0.66870$	$\textsf{none}$	0	$\Z/2\Z$	$\textsf{potential}$	$-28$	$N(\mathrm{U}(1))$	✓		✓	✓			$1$	$1$	$1$	$26.16385905$	0.874073183	$16581375$	$\bigl[a + 1$ , $a$ , $a + 1$ , $24 a - 72$ , $-113 a + 447\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(24a-72\right){x}-113a+447$
5.1-a1	5.1-a	$1$	$1$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	5.1	$5$	$- 5^{9}$	$0.99994$	$(-a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Nn	$1$	$1$	$1$	$11.70663218$	1.564364528	$\frac{534684321}{1953125} a + \frac{3601913643}{1953125}$	$\bigl[1$ , $-1$ , $a$ , $-15 a - 54$ , $-33 a - 127\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-15a-54\right){x}-33a-127$
5.1-b1	5.1-b	$1$	$1$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	5.1	$5$	$- 5^{9}$	$0.99994$	$(-a+3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Nn	$1$	$3^{2}$	$0.053182667$	$11.35679518$	1.452795207	$\frac{534684321}{1953125} a + \frac{3601913643}{1953125}$	$\bigl[1$ , $-1$ , $0$ , $-8 a + 30$ , $27 a - 101\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-8a+30\right){x}+27a-101$
5.2-a1	5.2-a	$1$	$1$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	5.2	$5$	$- 5^{9}$	$0.99994$	$(-a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Nn	$1$	$1$	$1$	$11.70663218$	1.564364528	$-\frac{534684321}{1953125} a + \frac{3601913643}{1953125}$	$\bigl[1$ , $-1$ , $a$ , $14 a - 54$ , $33 a - 127\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(14a-54\right){x}+33a-127$
5.2-b1	5.2-b	$1$	$1$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	5.2	$5$	$- 5^{9}$	$0.99994$	$(-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3Nn	$1$	$3^{2}$	$0.053182667$	$11.35679518$	1.452795207	$-\frac{534684321}{1953125} a + \frac{3601913643}{1953125}$	$\bigl[1$ , $-1$ , $0$ , $8 a + 30$ , $-27 a - 101\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(8a+30\right){x}-27a-101$
10.1-a1	10.1-a	$2$	$3$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{4} \cdot 5$	$1.18914$	$(-a+4), (-a+3)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.1	$1$	$2$	$1$	$36.43104508$	1.081845150	$\frac{5689}{20} a + \frac{21627}{20}$	$\bigl[1$ , $0$ , $1$ , $-2 a + 7$ , $-30 a + 112\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-2a+7\right){x}-30a+112$
10.1-a2	10.1-a	$2$	$3$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{12} \cdot 5^{3}$	$1.18914$	$(-a+4), (-a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.2	$1$	$2$	$1$	$4.047893897$	1.081845150	$\frac{18258829169}{8000} a + \frac{68318145777}{8000}$	$\bigl[1$ , $0$ , $1$ , $18 a - 68$ , $814 a - 3046\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(18a-68\right){x}+814a-3046$
10.1-b1	10.1-b	$2$	$5$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{10} \cdot 5^{5}$	$1.18914$	$(-a+4), (-a+3)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.1	$1$	$2 \cdot 5^{2}$	$1$	$8.284026412$	2.213999186	$\frac{73603923}{100000} a + \frac{358833109}{100000}$	$\bigl[a + 1$ , $a - 1$ , $a + 1$ , $-27 a - 102$ , $-216 a - 811\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-27a-102\right){x}-216a-811$
10.1-b2	10.1-b	$2$	$5$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{2} \cdot 5$	$1.18914$	$(-a+4), (-a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.2	$25$	$2$	$1$	$0.331361056$	2.213999186	$\frac{7114676554418062503}{10} a + \frac{26620682081199569989}{10}$	$\bigl[a + 1$ , $a - 1$ , $a + 1$ , $-17217 a - 64432$ , $-2427316 a - 9082191\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-17217a-64432\right){x}-2427316a-9082191$
10.1-c1	10.1-c	$2$	$5$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{10} \cdot 5^{5}$	$1.18914$	$(-a+4), (-a+3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.4.1	$1$	$2 \cdot 5$	$0.054400494$	$14.16313473$	2.059198521	$\frac{73603923}{100000} a + \frac{358833109}{100000}$	$\bigl[a + 1$ , $0$ , $0$ , $-5 a + 29$ , $-20 a + 81\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a+29\right){x}-20a+81$
10.1-c2	10.1-c	$2$	$5$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{2} \cdot 5$	$1.18914$	$(-a+4), (-a+3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.4.2	$1$	$2$	$0.272002473$	$14.16313473$	2.059198521	$\frac{7114676554418062503}{10} a + \frac{26620682081199569989}{10}$	$\bigl[a + 1$ , $0$ , $0$ , $1285 a - 4941$ , $-48650 a + 182431\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(1285a-4941\right){x}-48650a+182431$
10.1-d1	10.1-d	$2$	$3$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{4} \cdot 5$	$1.18914$	$(-a+4), (-a+3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	$2$	$0.115049867$	$20.19548844$	1.241956719	$\frac{5689}{20} a + \frac{21627}{20}$	$\bigl[1$ , $-a - 1$ , $0$ , $3$ , $1\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+3{x}+1$
10.1-d2	10.1-d	$2$	$3$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.1	$2 \cdot 5$	$- 2^{12} \cdot 5^{3}$	$1.18914$	$(-a+4), (-a+3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	$2 \cdot 3$	$0.038349955$	$20.19548844$	1.241956719	$\frac{18258829169}{8000} a + \frac{68318145777}{8000}$	$\bigl[1$ , $-a - 1$ , $0$ , $-20 a - 72$ , $128 a + 480\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-20a-72\right){x}+128a+480$
10.2-a1	10.2-a	$2$	$3$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{12} \cdot 5^{3}$	$1.18914$	$(-a+4), (-a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.2	$1$	$2$	$1$	$4.047893897$	1.081845150	$-\frac{18258829169}{8000} a + \frac{68318145777}{8000}$	$\bigl[1$ , $0$ , $1$ , $-18 a - 68$ , $-814 a - 3046\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-18a-68\right){x}-814a-3046$
10.2-a2	10.2-a	$2$	$3$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{4} \cdot 5$	$1.18914$	$(-a+4), (-a-3)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.1	$1$	$2$	$1$	$36.43104508$	1.081845150	$-\frac{5689}{20} a + \frac{21627}{20}$	$\bigl[1$ , $0$ , $1$ , $2 a + 7$ , $30 a + 112\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(2a+7\right){x}+30a+112$
10.2-b1	10.2-b	$2$	$5$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{2} \cdot 5$	$1.18914$	$(-a+4), (-a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.2	$25$	$2$	$1$	$0.331361056$	2.213999186	$-\frac{7114676554418062503}{10} a + \frac{26620682081199569989}{10}$	$\bigl[a + 1$ , $a - 1$ , $1$ , $17221 a - 64425$ , $2362884 a - 8841125\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(17221a-64425\right){x}+2362884a-8841125$
10.2-b2	10.2-b	$2$	$5$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{10} \cdot 5^{5}$	$1.18914$	$(-a+4), (-a-3)$	0	$\Z/5\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.1.1	$1$	$2 \cdot 5^{2}$	$1$	$8.284026412$	2.213999186	$-\frac{73603923}{100000} a + \frac{358833109}{100000}$	$\bigl[a + 1$ , $a - 1$ , $1$ , $31 a - 95$ , $114 a - 405\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(31a-95\right){x}+114a-405$
10.2-c1	10.2-c	$2$	$5$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{2} \cdot 5$	$1.18914$	$(-a+4), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.4.2	$1$	$2$	$0.272002473$	$14.16313473$	2.059198521	$-\frac{7114676554418062503}{10} a + \frac{26620682081199569989}{10}$	$\bigl[a + 1$ , $-a$ , $0$ , $-1285 a - 4941$ , $48650 a + 182431\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-1285a-4941\right){x}+48650a+182431$
10.2-c2	10.2-c	$2$	$5$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{10} \cdot 5^{5}$	$1.18914$	$(-a+4), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$5$	5B.4.1	$1$	$2 \cdot 5$	$0.054400494$	$14.16313473$	2.059198521	$-\frac{73603923}{100000} a + \frac{358833109}{100000}$	$\bigl[a + 1$ , $-a$ , $0$ , $5 a + 29$ , $20 a + 81\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(5a+29\right){x}+20a+81$
10.2-d1	10.2-d	$2$	$3$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{12} \cdot 5^{3}$	$1.18914$	$(-a+4), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	$2 \cdot 3$	$0.038349955$	$20.19548844$	1.241956719	$-\frac{18258829169}{8000} a + \frac{68318145777}{8000}$	$\bigl[1$ , $a - 1$ , $0$ , $20 a - 72$ , $-128 a + 480\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(20a-72\right){x}-128a+480$
10.2-d2	10.2-d	$2$	$3$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	10.2	$2 \cdot 5$	$- 2^{4} \cdot 5$	$1.18914$	$(-a+4), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B	$1$	$2$	$0.115049867$	$20.19548844$	1.241956719	$-\frac{5689}{20} a + \frac{21627}{20}$	$\bigl[1$ , $a - 1$ , $0$ , $3$ , $1\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+3{x}+1$
14.1-a1	14.1-a	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{36} \cdot 7^{2}$	$1.29349$	$(-a+4), (-2a+7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$12.63051067$	$0.436190660$	1.472425245	$-\frac{548347731625}{1835008}$	$\bigl[1$ , $0$ , $1$ , $-171$ , $-874\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
14.1-a2	14.1-a	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{4} \cdot 7^{2}$	$1.29349$	$(-a+4), (-2a+7)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2}$	$1.403390075$	$35.33144352$	1.472425245	$-\frac{15625}{28}$	$\bigl[1$ , $0$ , $1$ , $-1$ , $0\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-{x}$
14.1-a3	14.1-a	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{12} \cdot 7^{6}$	$1.29349$	$(-a+4), (-2a+7)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2^{2} \cdot 3$	$4.210170225$	$3.925715946$	1.472425245	$\frac{9938375}{21952}$	$\bigl[1$ , $0$ , $1$ , $4$ , $-6\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
14.1-a4	14.1-a	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{6} \cdot 7^{12}$	$1.29349$	$(-a+4), (-2a+7)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2^{3} \cdot 3$	$2.105085112$	$3.925715946$	1.472425245	$\frac{4956477625}{941192}$	$\bigl[1$ , $0$ , $1$ , $-36$ , $-70\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
14.1-a5	14.1-a	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{2} \cdot 7^{4}$	$1.29349$	$(-a+4), (-2a+7)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2^{3}$	$0.701695037$	$35.33144352$	1.472425245	$\frac{128787625}{98}$	$\bigl[1$ , $0$ , $1$ , $-11$ , $12\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
14.1-a6	14.1-a	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{18} \cdot 7^{4}$	$1.29349$	$(-a+4), (-2a+7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	$2^{3}$	$6.315255337$	$0.436190660$	1.472425245	$\frac{2251439055699625}{25088}$	$\bigl[1$ , $0$ , $1$ , $-2731$ , $-55146\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
14.1-b1	14.1-b	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{36} \cdot 7^{2}$	$1.29349$	$(-a+4), (-2a+7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$7.027708105$	0.939116998	$-\frac{548347731625}{1835008}$	$\bigl[1$ , $a - 1$ , $0$ , $20462 a - 76559$ , $-3121544 a + 11679749\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(20462a-76559\right){x}-3121544a+11679749$
14.1-b2	14.1-b	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{4} \cdot 7^{2}$	$1.29349$	$(-a+4), (-2a+7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$7.027708105$	0.939116998	$-\frac{15625}{28}$	$\bigl[1$ , $a - 1$ , $0$ , $62 a - 229$ , $960 a - 3591\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(62a-229\right){x}+960a-3591$
14.1-b3	14.1-b	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{12} \cdot 7^{6}$	$1.29349$	$(-a+4), (-2a+7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	$2^{2}$	$1$	$7.027708105$	0.939116998	$\frac{9938375}{21952}$	$\bigl[1$ , $a - 1$ , $0$ , $-538 a + 2016$ , $-21216 a + 79384\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-538a+2016\right){x}-21216a+79384$
14.1-b4	14.1-b	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{6} \cdot 7^{12}$	$1.29349$	$(-a+4), (-2a+7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs	$1$	$2^{2}$	$1$	$7.027708105$	0.939116998	$\frac{4956477625}{941192}$	$\bigl[1$ , $a - 1$ , $0$ , $4262 a - 15944$ , $-246560 a + 922544\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4262a-15944\right){x}-246560a+922544$
14.1-b5	14.1-b	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{2} \cdot 7^{4}$	$1.29349$	$(-a+4), (-2a+7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$7.027708105$	0.939116998	$\frac{128787625}{98}$	$\bigl[1$ , $a - 1$ , $0$ , $1262 a - 4719$ , $45312 a - 169541\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1262a-4719\right){x}+45312a-169541$
14.1-b6	14.1-b	$6$	$18$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	14.1	$2 \cdot 7$	$2^{18} \cdot 7^{4}$	$1.29349$	$(-a+4), (-2a+7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B	$1$	$2^{2}$	$1$	$7.027708105$	0.939116998	$\frac{2251439055699625}{25088}$	$\bigl[1$ , $a - 1$ , $0$ , $327662 a - 1225999$ , $-197976456 a + 740760069\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(327662a-1225999\right){x}-197976456a+740760069$
16.1-a1	16.1-a	$4$	$14$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{12}$	$1.33740$	$(-a+4)$	0	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓			✓			$1$	$2^{2}$	$1$	$13.08192952$	1.748146366	$-3375$	$\bigl[a$ , $1$ , $a$ , $-5 a - 19$ , $7 a + 26\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a-19\right){x}+7a+26$
16.1-a2	16.1-a	$4$	$14$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{12}$	$1.33740$	$(-a+4)$	0	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓			✓			$1$	$2^{2}$	$1$	$13.08192952$	1.748146366	$-3375$	$\bigl[a$ , $1$ , $a$ , $5 a - 19$ , $-7 a + 26\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(5a-19\right){x}-7a+26$
16.1-a3	16.1-a	$4$	$14$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{12}$	$1.33740$	$(-a+4)$	0	$\Z/2\Z$	$\textsf{potential}$	$-28$	$N(\mathrm{U}(1))$	✓			✓			$1$	$2^{2}$	$1$	$13.08192952$	1.748146366	$16581375$	$\bigl[a$ , $1$ , $a$ , $-85 a - 319$ , $699 a + 2614\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-85a-319\right){x}+699a+2614$
16.1-a4	16.1-a	$4$	$14$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	16.1	$2^{4}$	$2^{12}$	$1.33740$	$(-a+4)$	0	$\Z/2\Z$	$\textsf{potential}$	$-28$	$N(\mathrm{U}(1))$	✓			✓			$1$	$2^{2}$	$1$	$13.08192952$	1.748146366	$16581375$	$\bigl[a$ , $1$ , $a$ , $85 a - 319$ , $-699 a + 2614\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(85a-319\right){x}-699a+2614$
18.1-a1	18.1-a	$2$	$2$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	18.1	$2 \cdot 3^{2}$	$2^{8} \cdot 3^{8}$	$1.37737$	$(-a+4), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$1$	$2^{2}$	$1$	$8.501880177$	1.136111527	$\frac{4913}{1296}$	$\bigl[a + 1$ , $-a - 1$ , $a$ , $2$ , $-38 a - 142\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+2{x}-38a-142$
18.1-a2	18.1-a	$2$	$2$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	18.1	$2 \cdot 3^{2}$	$2^{4} \cdot 3^{16}$	$1.37737$	$(-a+4), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$1$	$2^{2}$	$1$	$8.501880177$	1.136111527	$\frac{838561807}{26244}$	$\bigl[a + 1$ , $-a - 1$ , $a$ , $-80 a - 298$ , $-738 a - 2762\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-80a-298\right){x}-738a-2762$
18.1-b1	18.1-b	$2$	$2$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	18.1	$2 \cdot 3^{2}$	$2^{8} \cdot 3^{8}$	$1.37737$	$(-a+4), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$1$	$2^{2}$	$1$	$8.501880177$	1.136111527	$\frac{4913}{1296}$	$\bigl[a + 1$ , $-1$ , $a$ , $-a + 2$ , $38 a - 142\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a+2\right){x}+38a-142$
18.1-b2	18.1-b	$2$	$2$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	18.1	$2 \cdot 3^{2}$	$2^{4} \cdot 3^{16}$	$1.37737$	$(-a+4), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2$	2B	$1$	$2^{2}$	$1$	$8.501880177$	1.136111527	$\frac{838561807}{26244}$	$\bigl[a + 1$ , $-1$ , $a$ , $79 a - 298$ , $738 a - 2762\bigr]$	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(79a-298\right){x}+738a-2762$
20.1-a1	20.1-a	$1$	$1$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	20.1	$2^{2} \cdot 5$	$- 2^{8} \cdot 5$	$1.41413$	$(-a+4), (-a+3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	$1$	$1$	$13.92592824$	1.860930439	$\frac{3236}{5} a + \frac{12108}{5}$	$\bigl[a$ , $-a + 1$ , $0$ , $-13 a - 26$ , $-32 a - 99\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-13a-26\right){x}-32a-99$
20.1-b1	20.1-b	$1$	$1$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	20.1	$2^{2} \cdot 5$	$- 2^{8} \cdot 5$	$1.41413$	$(-a+4), (-a+3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	$1$	$0.223019342$	$31.97666518$	1.905950784	$\frac{3236}{5} a + \frac{12108}{5}$	$\bigl[a$ , $-1$ , $0$ , $2$ , $-2 a + 8\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}-2a+8$
20.2-a1	20.2-a	$1$	$1$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	20.2	$2^{2} \cdot 5$	$- 2^{8} \cdot 5$	$1.41413$	$(-a+4), (-a-3)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	$1$	$1$	$13.92592824$	1.860930439	$-\frac{3236}{5} a + \frac{12108}{5}$	$\bigl[a$ , $a + 1$ , $0$ , $13 a - 26$ , $32 a - 99\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(13a-26\right){x}+32a-99$
20.2-b1	20.2-b	$1$	$1$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	20.2	$2^{2} \cdot 5$	$- 2^{8} \cdot 5$	$1.41413$	$(-a+4), (-a-3)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	$1$	$0.223019342$	$31.97666518$	1.905950784	$-\frac{3236}{5} a + \frac{12108}{5}$	$\bigl[a$ , $-1$ , $0$ , $2$ , $2 a + 8\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+2{x}+2a+8$
22.1-a1	22.1-a	$2$	$2$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	22.1	$2 \cdot 11$	$2^{4} \cdot 11^{2}$	$1.44823$	$(-a+4), (a-5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2}$	$0.350694013$	$18.00713737$	1.687753482	$\frac{69372345}{242} a - \frac{519137881}{484}$	$\bigl[a + 1$ , $-a$ , $a + 1$ , $-28 a - 98$ , $-2405 a - 8994\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-28a-98\right){x}-2405a-8994$
22.1-a2	22.1-a	$2$	$2$	$\Q(\sqrt{14})$	$2$	$[2, 0]$	22.1	$2 \cdot 11$	$2^{2} \cdot 11$	$1.44823$	$(-a+4), (a-5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$0.701388027$	$18.00713737$	1.687753482	$-\frac{13538239447075}{22} a + \frac{50655455887741}{22}$	$\bigl[a + 1$ , $-a$ , $a + 1$ , $-1538 a - 5748$ , $-63797 a - 238702\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-1538a-5748\right){x}-63797a-238702$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.