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
18144.1-b1	18144.1-b	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	18144.1	\( 2^{5} \cdot 3^{4} \cdot 7 \)	\( 2^{6} \cdot 3^{6} \cdot 7^{2} \)	$2.74392$	$(a), (-2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.267448971$	$3.427885657$	2.772095747	\( \frac{156735}{7} a - 4374 \)	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -3 a - 3\) , \( 9 a\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-3\right){x}+9a$
18144.1-c1	18144.1-c	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	18144.1	\( 2^{5} \cdot 3^{4} \cdot 7 \)	\( 2^{6} \cdot 3^{18} \cdot 7^{2} \)	$2.74392$	$(a), (-2a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$1.142628552$	1.727491994	\( \frac{156735}{7} a - 4374 \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -35 a - 29\) , \( -114 a - 7\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-35a-29\right){x}-114a-7$
36288.1-a1	36288.1-a	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	36288.1	\( 2^{6} \cdot 3^{4} \cdot 7 \)	\( 2^{12} \cdot 3^{18} \cdot 7^{2} \)	$3.26308$	$(a), (-2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1.198886294$	$0.807960397$	2.928930299	\( \frac{156735}{7} a - 4374 \)	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 6 a + 132\) , \( -485 a + 222\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a+132\right){x}-485a+222$
36288.1-d1	36288.1-d	$2$	$2$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	36288.1	\( 2^{6} \cdot 3^{4} \cdot 7 \)	\( 2^{12} \cdot 3^{6} \cdot 7^{2} \)	$3.26308$	$(a), (-2a+1), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.702246250$	$2.423881193$	5.146852535	\( \frac{156735}{7} a - 4374 \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( a + 16\) , \( 12 a - 17\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+16\right){x}+12a-17$

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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.