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
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-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	\( \frac{4956477625}{941192} \)	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 4262 a - 15944\) , \( -246560 a + 922544\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4262a-15944\right){x}-246560a+922544$
98.1-a4	98.1-a	$6$	$18$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{6} \cdot 7^{18} \)	$2.10397$	$(-a+4), (-2a+7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	\( 2^{3} \)	$2.451474306$	$1.985259457$	2.601420732	\( \frac{4956477625}{941192} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 993 a - 3721\) , \( 29312 a - 109675\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(993a-3721\right){x}+29312a-109675$
98.1-b4	98.1-b	$6$	$18$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	98.1	\( 2 \cdot 7^{2} \)	\( 2^{6} \cdot 7^{18} \)	$2.10397$	$(-a+4), (-2a+7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3Cs	$1$	\( 2^{3} \)	$2.451474306$	$1.985259457$	2.601420732	\( \frac{4956477625}{941192} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -993 a - 3721\) , \( -29312 a - 109675\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-993a-3721\right){x}-29312a-109675$
112.1-a4	112.1-a	$6$	$18$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	112.1	\( 2^{4} \cdot 7 \)	\( 2^{18} \cdot 7^{12} \)	$2.17539$	$(-a+4), (-2a+7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3Cs	$1$	\( 2^{4} \cdot 3 \)	$0.584534527$	$1.962857973$	3.679732717	\( \frac{4956477625}{941192} \)	\( \bigl[a\) , \( 0\) , \( a\) , \( -145\) , \( -702\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-145{x}-702$
112.1-f4	112.1-f	$6$	$18$	\(\Q(\sqrt{14}) \)	$2$	$[2, 0]$	112.1	\( 2^{4} \cdot 7 \)	\( 2^{18} \cdot 7^{12} \)	$2.17539$	$(-a+4), (-2a+7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3$	2B, 3Cs	$1$	\( 2^{3} \)	$1$	$3.513854052$	0.939116998	\( \frac{4956477625}{941192} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 17047 a - 63784\) , \( -1874592 a + 7014081\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17047a-63784\right){x}-1874592a+7014081$

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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.