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
54.3-c1	54.3-c	$2$	$3$	\(\Q(\sqrt{19}) \)	$2$	$[2, 0]$	54.3	\( 2 \cdot 3^{3} \)	\( 2 \cdot 3^{3} \)	$2.11176$	$(-3a+13), (-a+4)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$1$	\( 1 \)	$3.251828187$	$4.640027631$	3.461555965	\( \frac{713875}{2} a - \frac{3112375}{2} \)	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 3\) , \( -3 a - 14\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+3{x}-3a-14$
54.3-f1	54.3-f	$2$	$3$	\(\Q(\sqrt{19}) \)	$2$	$[2, 0]$	54.3	\( 2 \cdot 3^{3} \)	\( 2 \cdot 3^{3} \)	$2.11176$	$(-3a+13), (-a+4)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 1 \)	$0.314981619$	$47.65387234$	3.443551701	\( \frac{713875}{2} a - \frac{3112375}{2} \)	\( \bigl[a\) , \( -a\) , \( 0\) , \( -4 a + 10\) , \( -a + 23\bigr] \)	${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-4a+10\right){x}-a+23$

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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.