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
19.1-a3	19.1-a	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	19.1	\( 19 \)	\( - 19^{3} \)	$1.77580$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	\( 3 \)	$1$	$10.97341480$	0.676506855	\( -\frac{72241514230136832}{6859} a^{2} + \frac{49766614320668672}{6859} a + \frac{232207325676879872}{6859} \)	\( \bigl[0\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( 20 a^{2} - 9 a - 70\) , \( 81 a^{2} - 52 a - 273\bigr] \)	${y}^2+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(20a^{2}-9a-70\right){x}+81a^{2}-52a-273$
304.1-e3	304.1-e	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	304.1	\( 2^{4} \cdot 19 \)	\( - 2^{12} \cdot 19^{3} \)	$2.81891$	$(a^2-a-2), (-a^2-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 1 \)	$3.160345575$	$11.35659224$	2.212651479	\( -\frac{72241514230136832}{6859} a^{2} + \frac{49766614320668672}{6859} a + \frac{232207325676879872}{6859} \)	\( \bigl[0\) , \( a^{2} - a - 2\) , \( 0\) , \( 19 a^{2} - 59\) , \( 51 a^{2} - 24 a - 128\bigr] \)	${y}^2={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(19a^{2}-59\right){x}+51a^{2}-24a-128$
361.2-c3	361.2-c	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	361.2	\( 19^{2} \)	\( - 19^{9} \)	$2.90082$	$(-a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$9$	\( 2 \)	$1$	$3.046308799$	1.126822683	\( -\frac{72241514230136832}{6859} a^{2} + \frac{49766614320668672}{6859} a + \frac{232207325676879872}{6859} \)	\( \bigl[0\) , \( -a^{2} + 2 a + 1\) , \( a\) , \( 54 a^{2} + 87 a - 439\) , \( 548 a^{2} + 456 a - 3568\bigr] \)	${y}^2+a{y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(54a^{2}+87a-439\right){x}+548a^{2}+456a-3568$
475.2-b3	475.2-b	$4$	$6$	3.3.148.1	$3$	$[3, 0]$	475.2	\( 5^{2} \cdot 19 \)	\( - 5^{6} \cdot 19^{3} \)	$3.03658$	$(a^2-a-1), (-a^2-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 3$	2B, 3B	$1$	\( 2 \)	$0.413372433$	$41.66829336$	2.123770703	\( -\frac{72241514230136832}{6859} a^{2} + \frac{49766614320668672}{6859} a + \frac{232207325676879872}{6859} \)	\( \bigl[0\) , \( -a^{2} + a + 3\) , \( a\) , \( -25 a^{2} + 79 a - 29\) , \( 165 a^{2} - 431 a + 121\bigr] \)	${y}^2+a{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-25a^{2}+79a-29\right){x}+165a^{2}-431a+121$

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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.