Elliptic curve search results

Results (4 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
56.1-b4	56.1-b	$6$	$8$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	56.1	\( 2^{3} \cdot 7 \)	\( 2^{8} \cdot 7^{4} \)	$1.82928$	$(-a+4), (-2a+7)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$0.966528616$	$24.47471212$	3.161100443	\( \frac{740772}{49} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -570 a - 2133\) , \( 12630 a + 47257\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-570a-2133\right){x}+12630a+47257$
56.1-d4	56.1-d	$6$	$8$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	56.1	\( 2^{3} \cdot 7 \)	\( 2^{8} \cdot 7^{4} \)	$1.82928$	$(-a+4), (-2a+7)$	$2$	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$2.022709596$	$10.54517411$	2.850317744	\( \frac{740772}{49} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -11\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-5{x}-11$
112.1-b4	112.1-b	$6$	$8$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	112.1	\( 2^{4} \cdot 7 \)	\( 2^{8} \cdot 7^{4} \)	$2.17539$	$(-a+4), (-2a+7)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$4$	\( 2^{3} \)	$1$	$10.54517411$	2.818316330	\( \frac{740772}{49} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( -570 a - 2126\) , \( -14340 a - 53652\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-570a-2126\right){x}-14340a-53652$
112.1-e4	112.1-e	$6$	$8$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	112.1	\( 2^{4} \cdot 7 \)	\( 2^{8} \cdot 7^{4} \)	$2.17539$	$(-a+4), (-2a+7)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{2} \)	$1.393477166$	$24.47471212$	2.278732990	\( \frac{740772}{49} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 2\) , \( 0\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+2{x}$

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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.