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
13122.5-d3	13122.5-d	$4$	$21$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	13122.5	\( 2 \cdot 3^{8} \)	\( 2^{42} \cdot 3^{20} \)	$2.70510$	$(a), (-a-1), (a-1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3, 7$	2Cn, 3B.1.2, 7B	$1$	\( 2 \)	$6.303359192$	$0.194495073$	3.467573330	\( -\frac{1159088625}{2097152} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -852\) , \( 19664\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-852{x}+19664$
13122.5-e3	13122.5-e	$4$	$21$	\(\Q(\sqrt{-2}) \)	$2$	$[0, 1]$	13122.5	\( 2 \cdot 3^{8} \)	\( 2^{42} \cdot 3^{8} \)	$2.70510$	$(a), (-a-1), (a-1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2, 3, 7$	2Cn, 3B.1.1, 7B.2.3	$1$	\( 2 \cdot 3 \cdot 7 \)	$1$	$0.583485219$	1.925402993	\( -\frac{1159088625}{2097152} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -697\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-95{x}-697$

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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.