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
20.1-a5	20.1-a	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	20.1	\( 2^{2} \cdot 5 \)	\( 2^{8} \cdot 5^{8} \)	$1.79105$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2 \cdot 3 \)	$1$	$56.24286296$	0.770522476	\( \frac{148445904580292}{390625} a^{2} + \frac{173694846086594}{390625} a - \frac{68405381268774}{390625} \)	\( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( -898838 a^{2} - 1051718 a + 414194\) , \( 854513176 a^{2} + 999854320 a - 393769180\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-898838a^{2}-1051718a+414194\right){x}+854513176a^{2}+999854320a-393769180$
80.1-b11	80.1-b	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	80.1	\( 2^{4} \cdot 5 \)	\( 2^{8} \cdot 5^{8} \)	$2.25658$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{3} \)	$1$	$7.086151713$	1.164956165	\( \frac{148445904580292}{390625} a^{2} + \frac{173694846086594}{390625} a - \frac{68405381268774}{390625} \)	\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a^{2} - 1\) , \( -6597627 a^{2} - 7719793 a + 3040262\) , \( -16993318815 a^{2} - 19883652708 a + 7830710398\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-6597627a^{2}-7719793a+3040262\right){x}-16993318815a^{2}-19883652708a+7830710398$
100.2-a7	100.2-a	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	100.2	\( 2^{2} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{14} \)	$2.34209$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1$	$14.18378554$	1.165899989	\( \frac{148445904580292}{390625} a^{2} + \frac{173694846086594}{390625} a - \frac{68405381268774}{390625} \)	\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a + 1\) , \( -10028115 a^{2} - 11733760 a + 4621070\) , \( 31833826821 a^{2} + 37248330581 a - 14669381620\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10028115a^{2}-11733760a+4621070\right){x}+31833826821a^{2}+37248330581a-14669381620$
400.2-e11	400.2-e	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	400.2	\( 2^{4} \cdot 5^{2} \)	\( 2^{8} \cdot 5^{14} \)	$2.95084$	$(a^2-a-2), (a^2-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1.036608788$	$9.463618135$	2.419148294	\( \frac{148445904580292}{390625} a^{2} + \frac{173694846086594}{390625} a - \frac{68405381268774}{390625} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( a^{2} - 1\) , \( -73608095 a^{2} - 86127837 a + 33919430\) , \( -633264406060 a^{2} - 740974123992 a + 291815284765\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-73608095a^{2}-86127837a+33919430\right){x}-633264406060a^{2}-740974123992a+291815284765$

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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.