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-a1	20.1-a	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	20.1	\( 2^{2} \cdot 5 \)	\( - 2^{8} \cdot 5^{2} \)	$1.79105$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B.1.1	$1$	\( 2 \cdot 3 \)	$1$	$56.24286296$	0.770522476	\( \frac{13838352792668}{25} a^{2} - \frac{34335804621874}{25} a + \frac{9343051795654}{25} \)	\( \bigl[a^{2} - a - 2\) , \( 0\) , \( a^{2} - 1\) , \( 1292 a^{2} + 1512 a - 596\) , \( 38980968 a^{2} + 45611104 a - 17962864\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(1292a^{2}+1512a-596\right){x}+38980968a^{2}+45611104a-17962864$
80.1-b7	80.1-b	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	80.1	\( 2^{4} \cdot 5 \)	\( - 2^{8} \cdot 5^{2} \)	$2.25658$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$4$	\( 2 \)	$1$	$7.086151713$	1.164956165	\( \frac{13838352792668}{25} a^{2} - \frac{34335804621874}{25} a + \frac{9343051795654}{25} \)	\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a^{2} - 1\) , \( 9483 a^{2} + 11097 a - 4368\) , \( -775196971 a^{2} - 907047500 a + 357219390\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(9483a^{2}+11097a-4368\right){x}-775196971a^{2}-907047500a+357219390$
100.2-a3	100.2-a	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	100.2	\( 2^{2} \cdot 5^{2} \)	\( - 2^{8} \cdot 5^{8} \)	$2.34209$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1$	$14.18378554$	1.165899989	\( \frac{13838352792668}{25} a^{2} - \frac{34335804621874}{25} a + \frac{9343051795654}{25} \)	\( \bigl[a^{2} - a - 2\) , \( a + 1\) , \( a + 1\) , \( 14415 a^{2} + 16870 a - 6640\) , \( 1452659431 a^{2} + 1699737171 a - 669401630\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(14415a^{2}+16870a-6640\right){x}+1452659431a^{2}+1699737171a-669401630$
400.2-e7	400.2-e	$12$	$24$	3.3.148.1	$3$	$[3, 0]$	400.2	\( 2^{4} \cdot 5^{2} \)	\( - 2^{8} \cdot 5^{8} \)	$2.95084$	$(a^2-a-2), (a^2-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$0.259152197$	$37.85447254$	2.419148294	\( \frac{13838352792668}{25} a^{2} - \frac{34335804621874}{25} a + \frac{9343051795654}{25} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( a^{2} - 1\) , \( 105815 a^{2} + 123813 a - 48760\) , \( -28888097400 a^{2} - 33801572392 a + 13311956725\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(105815a^{2}+123813a-48760\right){x}-28888097400a^{2}-33801572392a+13311956725$

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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.