Elliptic curve search results

Results (6 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
63.1-a5	63.1-a	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	63.1	\( 3^{2} \cdot 7 \)	\( 3^{16} \cdot 7^{2} \)	$1.33215$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z\oplus\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{7} \)	$1$	$13.02432697$	1.230683220	\( \frac{6570725617}{45927} \)	\( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \)	${y}^2+{x}{y}={x}^{3}-39{x}+90$
63.1-b5	63.1-b	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	63.1	\( 3^{2} \cdot 7 \)	\( 3^{16} \cdot 7^{2} \)	$1.33215$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2^{3} \)	$1.492598417$	$3.651881942$	1.030103091	\( \frac{6570725617}{45927} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -40\) , \( -130\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-40{x}-130$
441.1-a5	441.1-a	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	441.1	\( 3^{2} \cdot 7^{2} \)	\( 3^{16} \cdot 7^{8} \)	$2.16684$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{6} \)	$1$	$2.606675619$	1.970461553	\( \frac{6570725617}{45927} \)	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -13111 a - 34687\) , \( 1336023 a + 3534782\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13111a-34687\right){x}+1336023a+3534782$
441.1-f5	441.1-f	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	441.1	\( 3^{2} \cdot 7^{2} \)	\( 3^{16} \cdot 7^{8} \)	$2.16684$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2Cs	$1$	\( 2^{6} \)	$1$	$2.606675619$	1.970461553	\( \frac{6570725617}{45927} \)	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -13111 a - 34687\) , \( -1336023 a - 3534784\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-13111a-34687\right){x}-1336023a-3534784$
567.1-c5	567.1-c	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	567.1	\( 3^{4} \cdot 7 \)	\( 3^{28} \cdot 7^{2} \)	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{5} \)	$1.319254411$	$4.341442324$	4.329558047	\( \frac{6570725617}{45927} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -351\) , \( 2430\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-351{x}+2430$
567.1-l5	567.1-l	$8$	$16$	\(\Q(\sqrt{7}) \)	$2$	$[2, 0]$	567.1	\( 3^{4} \cdot 7 \)	\( 3^{28} \cdot 7^{2} \)	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{5} \)	$1$	$1.217293980$	1.840375511	\( \frac{6570725617}{45927} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-351{x}-2430$

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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.