Elliptic curve search results

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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
8.3-c1	8.3-c	$1$	$1$	4.4.19664.1	$4$	$[4, 0]$	8.3	\( 2^{3} \)	\( 2^{8} \)	$16.25028$	$(a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$0.227481585$	$394.8608628$	5.124416150	\( 768 a^{2} - 1024 a - 3328 \)	\( \bigl[0\) , \( a^{3} - 2 a^{2} - 5 a\) , \( a^{2} - 2 a - 2\) , \( -35 a^{3} + 87 a^{2} + 132 a - 131\) , \( -245 a^{3} + 616 a^{2} + 909 a - 961\bigr] \)	${y}^2+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a\right){x}^{2}+\left(-35a^{3}+87a^{2}+132a-131\right){x}-245a^{3}+616a^{2}+909a-961$
8.3-d1	8.3-d	$1$	$1$	4.4.19664.1	$4$	$[4, 0]$	8.3	\( 2^{3} \)	\( 2^{8} \)	$16.25028$	$(a)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓			$1$	\( 2 \)	$0.042027207$	$533.4422787$	1.279004365	\( 768 a^{2} - 1024 a - 3328 \)	\( \bigl[0\) , \( -a^{3} + 2 a^{2} + 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -35 a^{3} + 87 a^{2} + 132 a - 131\) , \( 245 a^{3} - 616 a^{2} - 909 a + 958\bigr] \)	${y}^2+\left(a^{3}-2a^{2}-4a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a\right){x}^{2}+\left(-35a^{3}+87a^{2}+132a-131\right){x}+245a^{3}-616a^{2}-909a+958$

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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.