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
19.3-a1	19.3-a	$1$	$1$	4.4.17725.1	$4$	$[4, 0]$	19.3	\( 19 \)	\( 19^{3} \)	$17.19000$	$(-a^2+2a+5)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓				$1$	\( 1 \)	$1$	$153.3581516$	1.151897256	\( -\frac{90275715}{6859} a^{3} - \frac{111729456}{6859} a^{2} + \frac{690658245}{6859} a + \frac{1072123074}{6859} \)	\( \bigl[a\) , \( -a^{2} + 6\) , \( a^{2} - a - 6\) , \( -10 a^{3} - 13 a^{2} + 76 a + 125\) , \( 51 a^{3} + 66 a^{2} - 392 a - 630\bigr] \)	${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-10a^{3}-13a^{2}+76a+125\right){x}+51a^{3}+66a^{2}-392a-630$

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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.