Elliptic curves over Q(−2)\Q(\sqrt{-2})

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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
9.1-CMa1	9.1-CMa	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9.1	$3^{2}$	$3^{6}$	$0.43777$	$(-a-1)$	0	$\Z/6\Z$	$\textsf{yes}$	$-8$	$\mathrm{U}(1)$	✓			✓	$3$	3Cs.1.1	$1$	$2$	$1$	$7.326567372$	0.287814748	$8000$	$\bigl[a$ , $-a + 1$ , $1$ , $-1$ , $0\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$
9.3-CMa1	9.3-CMa	$1$	$1$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	9.3	$3^{2}$	$3^{6}$	$0.43777$	$(a-1)$	0	$\Z/6\Z$	$\textsf{yes}$	$-8$	$\mathrm{U}(1)$	✓			✓	$3$	3Cs.1.1	$1$	$2$	$1$	$7.326567372$	0.287814748	$8000$	$\bigl[a$ , $a + 1$ , $1$ , $-a - 1$ , $0\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$
32.1-a1	32.1-a	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	32.1	$2^{5}$	$2^{12}$	$0.60113$	$(a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓	$2$	2Cs	$1$	$2$	$1$	$6.875185818$	0.607686314	$1728$	$\bigl[0$ , $0$ , $0$ , $-1$ , $0\bigr]$	${y}^2={x}^{3}-{x}$
32.1-a2	32.1-a	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	32.1	$2^{5}$	$2^{12}$	$0.60113$	$(a)$	0	$\Z/4\Z$	$\textsf{potential}$	$-4$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	$2$	$1$	$6.875185818$	0.607686314	$1728$	$\bigl[0$ , $0$ , $0$ , $1$ , $0\bigr]$	${y}^2={x}^{3}+{x}$
32.1-a3	32.1-a	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	32.1	$2^{5}$	$2^{6}$	$0.60113$	$(a)$	0	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	$2$	$1$	$6.875185818$	0.607686314	$287496$	$\bigl[a$ , $-1$ , $0$ , $-2$ , $3\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-2{x}+3$
32.1-a4	32.1-a	$4$	$4$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	32.1	$2^{5}$	$2^{6}$	$0.60113$	$(a)$	0	$\Z/4\Z$	$\textsf{potential}$	$-16$	$N(\mathrm{U}(1))$	✓	✓		✓			$1$	$2$	$1$	$6.875185818$	0.607686314	$287496$	$\bigl[a$ , $-1$ , $a$ , $-1$ , $0\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-{x}$
51.1-a1	51.1-a	$2$	$2$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	51.1	$3 \cdot 17$	$3^{2} \cdot 17^{2}$	$0.67542$	$(-a-1), (-2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2}$	$0.032029606$	$7.122411322$	0.322621752	$-\frac{1437952}{2601} a - \frac{95168}{2601}$	$\bigl[a$ , $a - 1$ , $1$ , $-a$ , $0\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$
51.1-a2	51.1-a	$2$	$2$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	51.1	$3 \cdot 17$	$3^{4} \cdot 17$	$0.67542$	$(-a-1), (-2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$0.064059212$	$7.122411322$	0.322621752	$\frac{4268288}{1377} a + \frac{2027584}{1377}$	$\bigl[a$ , $a - 1$ , $a + 1$ , $-2 a + 2$ , $0\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+2\right){x}$
51.4-a1	51.4-a	$2$	$2$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	51.4	$3 \cdot 17$	$3^{2} \cdot 17^{2}$	$0.67542$	$(a-1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2}$	$0.032029606$	$7.122411322$	0.322621752	$\frac{1437952}{2601} a - \frac{95168}{2601}$	$\bigl[a$ , $-a - 1$ , $1$ , $0$ , $0\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}$
51.4-a2	51.4-a	$2$	$2$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	51.4	$3 \cdot 17$	$3^{4} \cdot 17$	$0.67542$	$(a-1), (2a+3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$0.064059212$	$7.122411322$	0.322621752	$-\frac{4268288}{1377} a + \frac{2027584}{1377}$	$\bigl[a$ , $-a - 1$ , $a + 1$ , $a + 2$ , $-a\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-a$
54.1-a1	54.1-a	$4$	$27$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	54.1	$2 \cdot 3^{3}$	$2^{3} \cdot 3^{3}$	$0.68514$	$(a), (-a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3Cs.1.1	$1$	$1$	$1$	$8.206562124$	0.644768414	$\frac{6935}{4} a - \frac{9251}{2}$	$\bigl[1$ , $-a + 1$ , $0$ , $-a - 1$ , $-1\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a-1\right){x}-1$
54.1-a2	54.1-a	$4$	$27$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	54.1	$2 \cdot 3^{3}$	$2 \cdot 3^{5}$	$0.68514$	$(a), (-a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	$1$	$1$	$8.206562124$	0.644768414	$-\frac{269}{2} a + 1619$	$\bigl[a + 1$ , $0$ , $1$ , $-a - 1$ , $0\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}$
54.1-a3	54.1-a	$4$	$27$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	54.1	$2 \cdot 3^{3}$	$2^{27} \cdot 3^{11}$	$0.68514$	$(a), (-a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	$1$	$1$	$0.911840236$	0.644768414	$\frac{241123607}{16384} a + \frac{59710933}{8192}$	$\bigl[1$ , $-a + 1$ , $0$ , $-51 a + 69$ , $62 a + 339\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-51a+69\right){x}+62a+339$
54.1-a4	54.1-a	$4$	$27$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	54.1	$2 \cdot 3^{3}$	$2^{9} \cdot 3^{9}$	$0.68514$	$(a), (-a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3Cs.1.1	$1$	$3$	$1$	$2.735520708$	0.644768414	$-\frac{2628365}{32} a + \frac{183347}{16}$	$\bigl[1$ , $-a + 1$ , $0$ , $-11 a + 4$ , $-26\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-11a+4\right){x}-26$
54.4-a1	54.4-a	$4$	$27$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	54.4	$2 \cdot 3^{3}$	$2^{3} \cdot 3^{3}$	$0.68514$	$(a), (a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3Cs.1.1	$1$	$1$	$1$	$8.206562124$	0.644768414	$-\frac{6935}{4} a - \frac{9251}{2}$	$\bigl[1$ , $a + 1$ , $0$ , $a - 1$ , $-1\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-1\right){x}-1$
54.4-a2	54.4-a	$4$	$27$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	54.4	$2 \cdot 3^{3}$	$2 \cdot 3^{5}$	$0.68514$	$(a), (a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	$1$	$1$	$8.206562124$	0.644768414	$\frac{269}{2} a + 1619$	$\bigl[a + 1$ , $-a$ , $1$ , $-1$ , $0\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}-{x}$
54.4-a3	54.4-a	$4$	$27$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	54.4	$2 \cdot 3^{3}$	$2^{27} \cdot 3^{11}$	$0.68514$	$(a), (a-1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	$1$	$1$	$0.911840236$	0.644768414	$-\frac{241123607}{16384} a + \frac{59710933}{8192}$	$\bigl[1$ , $a + 1$ , $0$ , $51 a + 69$ , $-62 a + 339\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(51a+69\right){x}-62a+339$
54.4-a4	54.4-a	$4$	$27$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	54.4	$2 \cdot 3^{3}$	$2^{9} \cdot 3^{9}$	$0.68514$	$(a), (a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3Cs.1.1	$1$	$3$	$1$	$2.735520708$	0.644768414	$\frac{2628365}{32} a + \frac{183347}{16}$	$\bigl[1$ , $a + 1$ , $0$ , $11 a + 4$ , $-26\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a+4\right){x}-26$
72.2-a1	72.2-a	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	72.2	$2^{3} \cdot 3^{2}$	$2^{10} \cdot 3^{16}$	$0.73624$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$1$	$1.817673508$	0.642644632	$\frac{207646}{6561}$	$\bigl[a$ , $1$ , $a$ , $5$ , $23\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+5{x}+23$
72.2-a2	72.2-a	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	72.2	$2^{3} \cdot 3^{2}$	$2^{8} \cdot 3^{2}$	$0.73624$	$(a), (-a-1), (a-1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2$	$1$	$7.270694035$	0.642644632	$\frac{2048}{3}$	$\bigl[0$ , $-1$ , $0$ , $1$ , $0\bigr]$	${y}^2={x}^{3}-{x}^{2}+{x}$
72.2-a3	72.2-a	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	72.2	$2^{3} \cdot 3^{2}$	$2^{4} \cdot 3^{4}$	$0.73624$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{3}$	$1$	$7.270694035$	0.642644632	$\frac{35152}{9}$	$\bigl[a$ , $1$ , $a$ , $0$ , $0\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
72.2-a4	72.2-a	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	72.2	$2^{3} \cdot 3^{2}$	$2^{8} \cdot 3^{8}$	$0.73624$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	$2^{4}$	$1$	$3.635347017$	0.642644632	$\frac{1556068}{81}$	$\bigl[a$ , $1$ , $a$ , $-5$ , $5\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-5{x}+5$
72.2-a5	72.2-a	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	72.2	$2^{3} \cdot 3^{2}$	$2^{11} \cdot 3^{20}$	$0.73624$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1$	$0.908836754$	0.642644632	$-\frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721}$	$\bigl[a$ , $1$ , $a$ , $70 a + 85$ , $-98 a + 559\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(70a+85\right){x}-98a+559$
72.2-a6	72.2-a	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	72.2	$2^{3} \cdot 3^{2}$	$2^{11} \cdot 3^{20}$	$0.73624$	$(a), (-a-1), (a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$1$	$0.908836754$	0.642644632	$\frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721}$	$\bigl[a$ , $1$ , $a$ , $-70 a + 85$ , $98 a + 559\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-70a+85\right){x}+98a+559$
72.2-a7	72.2-a	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	72.2	$2^{3} \cdot 3^{2}$	$2^{8} \cdot 3^{2}$	$0.73624$	$(a), (-a-1), (a-1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{2}$	$1$	$3.635347017$	0.642644632	$\frac{28756228}{3}$	$\bigl[a$ , $1$ , $a$ , $-15$ , $-27\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-15{x}-27$
72.2-a8	72.2-a	$8$	$16$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	72.2	$2^{3} \cdot 3^{2}$	$2^{10} \cdot 3^{4}$	$0.73624$	$(a), (-a-1), (a-1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1$	$1.817673508$	0.642644632	$\frac{3065617154}{9}$	$\bigl[a$ , $1$ , $a$ , $-95$ , $347\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-95{x}+347$
98.1-a1	98.1-a	$6$	$18$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	98.1	$2 \cdot 7^{2}$	$2^{36} \cdot 7^{2}$	$0.79523$	$(a), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	$2$	$1$	$0.875417135$	0.309506696	$-\frac{548347731625}{1835008}$	$\bigl[1$ , $0$ , $1$ , $-171$ , $-874\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
98.1-a2	98.1-a	$6$	$18$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	98.1	$2 \cdot 7^{2}$	$2^{4} \cdot 7^{2}$	$0.79523$	$(a), (7)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2$	$1$	$7.878754216$	0.309506696	$-\frac{15625}{28}$	$\bigl[1$ , $0$ , $1$ , $-1$ , $0\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-{x}$
98.1-a3	98.1-a	$6$	$18$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	98.1	$2 \cdot 7^{2}$	$2^{12} \cdot 7^{6}$	$0.79523$	$(a), (7)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2 \cdot 3$	$1$	$2.626251405$	0.309506696	$\frac{9938375}{21952}$	$\bigl[1$ , $0$ , $1$ , $4$ , $-6\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
98.1-a4	98.1-a	$6$	$18$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	98.1	$2 \cdot 7^{2}$	$2^{6} \cdot 7^{12}$	$0.79523$	$(a), (7)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2^{2} \cdot 3$	$1$	$1.313125702$	0.309506696	$\frac{4956477625}{941192}$	$\bigl[1$ , $0$ , $1$ , $-36$ , $-70\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
98.1-a5	98.1-a	$6$	$18$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	98.1	$2 \cdot 7^{2}$	$2^{2} \cdot 7^{4}$	$0.79523$	$(a), (7)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2}$	$1$	$3.939377108$	0.309506696	$\frac{128787625}{98}$	$\bigl[1$ , $0$ , $1$ , $-11$ , $12\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
98.1-a6	98.1-a	$6$	$18$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	98.1	$2 \cdot 7^{2}$	$2^{18} \cdot 7^{4}$	$0.79523$	$(a), (7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$0.437708567$	0.309506696	$\frac{2251439055699625}{25088}$	$\bigl[1$ , $0$ , $1$ , $-2731$ , $-55146\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
99.3-a1	99.3-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.3	$3^{2} \cdot 11$	$3^{11} \cdot 11$	$0.79725$	$(-a-1), (a-1), (a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3}$	$1$	$1.697318412$	0.600092679	$\frac{3103043505622}{72171} a - \frac{541923582149}{72171}$	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $-12 a - 90$ , $71 a + 302\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12a-90\right){x}+71a+302$
99.3-a2	99.3-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.3	$3^{2} \cdot 11$	$3^{25} \cdot 11^{2}$	$0.79725$	$(-a-1), (a-1), (a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2}$	$1$	$0.848659206$	0.600092679	$\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201}$	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $3 a + 95$ , $251 a - 30\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a+95\right){x}+251a-30$
99.3-a3	99.3-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.3	$3^{2} \cdot 11$	$3^{10} \cdot 11^{2}$	$0.79725$	$(-a-1), (a-1), (a+3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{4}$	$1$	$3.394636825$	0.600092679	$-\frac{364612508}{88209} a - \frac{393162727}{88209}$	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $-2 a - 5$ , $a + 4\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-5\right){x}+a+4$
99.3-a4	99.3-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.3	$3^{2} \cdot 11$	$3^{5} \cdot 11$	$0.79725$	$(-a-1), (a-1), (a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$6.789273651$	0.600092679	$\frac{689288}{297} a - \frac{385271}{297}$	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $-2 a$ , $-a\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$
99.3-a5	99.3-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.3	$3^{2} \cdot 11$	$3^{14} \cdot 11^{4}$	$0.79725$	$(-a-1), (a-1), (a+3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{3}$	$1$	$1.697318412$	0.600092679	$\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681}$	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $8 a$ , $19 a + 22\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+8a{x}+19a+22$
99.3-a6	99.3-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.3	$3^{2} \cdot 11$	$3^{7} \cdot 11^{8}$	$0.79725$	$(-a-1), (a-1), (a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2}$	$1$	$0.848659206$	0.600092679	$-\frac{68547528581042953}{156267624249} a + \frac{367387425943146769}{156267624249}$	$\bigl[a + 1$ , $-a + 1$ , $a + 1$ , $173 a - 15$ , $859 a + 1006\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(173a-15\right){x}+859a+1006$
99.4-a1	99.4-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.4	$3^{2} \cdot 11$	$3^{11} \cdot 11$	$0.79725$	$(-a-1), (a-1), (a-3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3}$	$1$	$1.697318412$	0.600092679	$-\frac{3103043505622}{72171} a - \frac{541923582149}{72171}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $10 a - 90$ , $-72 a + 302\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(10a-90\right){x}-72a+302$
99.4-a2	99.4-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.4	$3^{2} \cdot 11$	$3^{25} \cdot 11^{2}$	$0.79725$	$(-a-1), (a-1), (a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2}$	$1$	$0.848659206$	0.600092679	$-\frac{139338897204254761}{34173973914201} a - \frac{247929747123659233}{34173973914201}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $-5 a + 95$ , $-252 a - 30\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5a+95\right){x}-252a-30$
99.4-a3	99.4-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.4	$3^{2} \cdot 11$	$3^{10} \cdot 11^{2}$	$0.79725$	$(-a-1), (a-1), (a-3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{4}$	$1$	$3.394636825$	0.600092679	$\frac{364612508}{88209} a - \frac{393162727}{88209}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $-5$ , $-2 a + 4\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-2a+4$
99.4-a4	99.4-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.4	$3^{2} \cdot 11$	$3^{5} \cdot 11$	$0.79725$	$(-a-1), (a-1), (a-3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$6.789273651$	0.600092679	$-\frac{689288}{297} a - \frac{385271}{297}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $0$ , $0\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$
99.4-a5	99.4-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.4	$3^{2} \cdot 11$	$3^{14} \cdot 11^{4}$	$0.79725$	$(-a-1), (a-1), (a-3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{3}$	$1$	$1.697318412$	0.600092679	$-\frac{1026305863102}{7780827681} a - \frac{7150733769793}{7780827681}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $-10 a$ , $-20 a + 22\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-10a{x}-20a+22$
99.4-a6	99.4-a	$6$	$8$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	99.4	$3^{2} \cdot 11$	$3^{7} \cdot 11^{8}$	$0.79725$	$(-a-1), (a-1), (a-3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{2}$	$1$	$0.848659206$	0.600092679	$\frac{68547528581042953}{156267624249} a + \frac{367387425943146769}{156267624249}$	$\bigl[a + 1$ , $1$ , $a + 1$ , $-175 a - 15$ , $-860 a + 1006\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-175a-15\right){x}-860a+1006$
100.1-a1	100.1-a	$4$	$6$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	100.1	$2^{2} \cdot 5^{2}$	$2^{4} \cdot 5^{12}$	$0.79925$	$(a), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.2	$1$	$2 \cdot 3$	$0.137812304$	$2.141031885$	0.625917922	$-\frac{20720464}{15625}$	$\bigl[a$ , $0$ , $a$ , $-8$ , $18\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}-8{x}+18$
100.1-a2	100.1-a	$4$	$6$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	100.1	$2^{2} \cdot 5^{2}$	$2^{4} \cdot 5^{4}$	$0.79925$	$(a), (5)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.1	$1$	$2 \cdot 3$	$0.413436914$	$6.423095656$	0.625917922	$\frac{21296}{25}$	$\bigl[a$ , $0$ , $a$ , $2$ , $0\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+2{x}$
100.1-a3	100.1-a	$4$	$6$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	100.1	$2^{2} \cdot 5^{2}$	$2^{8} \cdot 5^{2}$	$0.79925$	$(a), (5)$	$1$	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.1	$1$	$3$	$0.826873828$	$6.423095656$	0.625917922	$\frac{16384}{5}$	$\bigl[0$ , $1$ , $0$ , $-1$ , $0\bigr]$	${y}^2={x}^{3}+{x}^{2}-{x}$
100.1-a4	100.1-a	$4$	$6$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	100.1	$2^{2} \cdot 5^{2}$	$2^{8} \cdot 5^{6}$	$0.79925$	$(a), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3B.1.2	$1$	$3$	$0.275624609$	$2.141031885$	0.625917922	$\frac{488095744}{125}$	$\bigl[0$ , $1$ , $0$ , $-41$ , $-116\bigr]$	${y}^2={x}^{3}+{x}^{2}-41{x}-116$
108.2-a1	108.2-a	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	108.2	$2^{2} \cdot 3^{3}$	$2^{8} \cdot 3^{13}$	$0.81478$	$(a), (-a-1), (a-1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B.1.2	$1$	$2^{4}$	$1$	$1.488316936$	1.052398998	$-\frac{18202756}{81} a - \frac{253086988}{81}$	$\bigl[a$ , $-a + 1$ , $0$ , $-59 a + 4$ , $122 a - 261\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-59a+4\right){x}+122a-261$
108.2-a2	108.2-a	$8$	$12$	$\Q(\sqrt{-2})$	$2$	$[0, 1]$	108.2	$2^{2} \cdot 3^{3}$	$2^{8} \cdot 3^{13}$	$0.81478$	$(a), (-a-1), (a-1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B.1.1	$1$	$2^{2} \cdot 3^{2}$	$1$	$1.488316936$	1.052398998	$\frac{18202756}{81} a - \frac{253086988}{81}$	$\bigl[a$ , $-a + 1$ , $a$ , $-48 a + 49$ , $7 a + 265\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a+49\right){x}+7a+265$

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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.