Elliptic curve search results

Results (13 matches)

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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
75.1-a7	75.1-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	75.1	$3 \cdot 5^{2}$	$3^{2} \cdot 5^{2}$	$0.45547$	$(-2a+1), (5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2$	$1$	$2.235701712$	0.322695746	$\frac{56667352321}{15}$	$\bigl[1$ , $1$ , $1$ , $-80$ , $242\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
1875.1-b7	1875.1-b	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	1875.1	$3 \cdot 5^{4}$	$3^{2} \cdot 5^{14}$	$1.01847$	$(-2a+1), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1$	$0.447140342$	1.032626388	$\frac{56667352321}{15}$	$\bigl[1$ , $0$ , $1$ , $-2001$ , $34273\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-2001{x}+34273$
11025.1-c7	11025.1-c	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	11025.1	$3^{2} \cdot 5^{2} \cdot 7^{2}$	$3^{8} \cdot 5^{2} \cdot 7^{6}$	$1.58597$	$(-2a+1), (-3a+1), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{4}$	$1$	$0.487870110$	2.253375518	$\frac{56667352321}{15}$	$\bigl[a + 1$ , $-a - 1$ , $1$ , $1200 a + 720$ , $15971 a - 30723\bigr]$	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1200a+720\right){x}+15971a-30723$
11025.3-c7	11025.3-c	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	11025.3	$3^{2} \cdot 5^{2} \cdot 7^{2}$	$3^{8} \cdot 5^{2} \cdot 7^{6}$	$1.58597$	$(-2a+1), (3a-2), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{4}$	$1$	$0.487870110$	2.253375518	$\frac{56667352321}{15}$	$\bigl[a + 1$ , $a + 1$ , $0$ , $-718 a - 1201$ , $-17891 a - 14032\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-718a-1201\right){x}-17891a-14032$
12675.1-a7	12675.1-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	12675.1	$3 \cdot 5^{2} \cdot 13^{2}$	$3^{2} \cdot 5^{2} \cdot 13^{6}$	$1.64224$	$(-2a+1), (-4a+1), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$4$	$2^{2}$	$1$	$0.620072089$	2.863990301	$\frac{56667352321}{15}$	$\bigl[1$ , $a + 1$ , $1$ , $-639 a + 1200$ , $9839 a + 5397\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-639a+1200\right){x}+9839a+5397$
12675.3-a7	12675.3-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	12675.3	$3 \cdot 5^{2} \cdot 13^{2}$	$3^{2} \cdot 5^{2} \cdot 13^{6}$	$1.64224$	$(-2a+1), (4a-3), (5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$4$	$2^{2}$	$1$	$0.620072089$	2.863990301	$\frac{56667352321}{15}$	$\bigl[a$ , $-a - 1$ , $a$ , $-1200 a + 641$ , $-9279 a + 14036\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1200a+641\right){x}-9279a+14036$
19200.1-g7	19200.1-g	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	19200.1	$2^{8} \cdot 3 \cdot 5^{2}$	$2^{24} \cdot 3^{2} \cdot 5^{2}$	$1.82190$	$(-2a+1), (2), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1.300312843$	$0.558925428$	3.356843389	$\frac{56667352321}{15}$	$\bigl[0$ , $1$ , $0$ , $-1280$ , $-18060\bigr]$	${y}^2={x}^{3}+{x}^{2}-1280{x}-18060$
57600.1-j7	57600.1-j	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	57600.1	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{24} \cdot 3^{8} \cdot 5^{2}$	$2.39775$	$(-2a+1), (2), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$2.664660740$	$0.322695746$	3.971591054	$\frac{56667352321}{15}$	$\bigl[0$ , $-a - 1$ , $0$ , $-3840 a$ , $108360 a - 54180\bigr]$	${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-3840a{x}+108360a-54180$
57600.1-k7	57600.1-k	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	57600.1	$2^{8} \cdot 3^{2} \cdot 5^{2}$	$2^{24} \cdot 3^{8} \cdot 5^{2}$	$2.39775$	$(-2a+1), (2), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$2.664660740$	$0.322695746$	3.971591054	$\frac{56667352321}{15}$	$\bigl[0$ , $a + 1$ , $0$ , $3842 a - 3841$ , $-104519 a + 50339\bigr]$	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3842a-3841\right){x}-104519a+50339$
81225.1-a7	81225.1-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	81225.1	$3^{2} \cdot 5^{2} \cdot 19^{2}$	$3^{8} \cdot 5^{2} \cdot 19^{6}$	$2.61289$	$(-2a+1), (-5a+3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$2.013853729$	$0.296125925$	2.754442525	$\frac{56667352321}{15}$	$\bigl[a$ , $a$ , $a + 1$ , $-1201 a - 3841$ , $44286 a + 89262\bigr]$	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1201a-3841\right){x}+44286a+89262$
81225.3-a7	81225.3-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	81225.3	$3^{2} \cdot 5^{2} \cdot 19^{2}$	$3^{8} \cdot 5^{2} \cdot 19^{6}$	$2.61289$	$(-2a+1), (-5a+2), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$2.013853729$	$0.296125925$	2.754442525	$\frac{56667352321}{15}$	$\bigl[1$ , $a$ , $a$ , $3841 a + 1200$ , $-44287 a + 133549\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(3841a+1200\right){x}-44287a+133549$
102675.1-a7	102675.1-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	102675.1	$3 \cdot 5^{2} \cdot 37^{2}$	$3^{2} \cdot 5^{2} \cdot 37^{6}$	$2.77055$	$(-2a+1), (-7a+4), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$6.036317352$	$0.367547097$	5.123708641	$\frac{56667352321}{15}$	$\bigl[a + 1$ , $-a + 1$ , $0$ , $560 a + 2641$ , $-69511 a + 50796\bigr]$	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(560a+2641\right){x}-69511a+50796$
102675.3-a7	102675.3-a	$8$	$16$	$\Q(\sqrt{-3})$	$2$	$[0, 1]$	102675.3	$3 \cdot 5^{2} \cdot 37^{2}$	$3^{2} \cdot 5^{2} \cdot 37^{6}$	$2.77055$	$(-2a+1), (-7a+3), (5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{2}$	$6.036317352$	$0.367547097$	5.123708641	$\frac{56667352321}{15}$	$\bigl[1$ , $-a$ , $0$ , $3201 a - 2641$ , $69511 a - 18715\bigr]$	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(3201a-2641\right){x}+69511a-18715$

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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.