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
19.4-a1	19.4-a	$2$	$3$	4.4.17725.1	$4$	$[4, 0]$	19.4	\( 19 \)	\( -19 \)	$17.19000$	$(a^3-3a^2-5a+14)$	$0 \le r \le 1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.1		\( 1 \)	$1$	$460.0279088$	3.134026093	\( -\frac{14048}{19} a^{3} - 869 a^{2} + \frac{128771}{19} a + \frac{239534}{19} \)	\( \bigl[a^{2} - 6\) , \( -a^{3} + a^{2} + 6 a\) , \( a^{3} - a^{2} - 7 a\) , \( -3 a^{3} + 7 a^{2} + 13 a - 16\) , \( -4 a^{3} + 19 a^{2} + 6 a - 84\bigr] \)	${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{3}-a^{2}-7a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(-3a^{3}+7a^{2}+13a-16\right){x}-4a^{3}+19a^{2}+6a-84$

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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.