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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
89.3-a1	89.3-a	$2$	$3$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	89.3	\( 89 \)	\( -89 \)	$5.25277$	$(-2a^3+a^2+7a-2)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.1	$1$	\( 1 \)	$1$	$377.6442939$	1.251019722	\( -\frac{79441}{89} a^{3} - \frac{10986}{89} a^{2} + \frac{246723}{89} a + \frac{51251}{89} \)	\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{3} - 2 a + 1\) , \( -a + 2\) , \( -a^{3} - a^{2} + 3 a\bigr] \)	${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(-a+2\right){x}-a^{3}-a^{2}+3a$
89.3-b2	89.3-b	$2$	$3$	\(\Q(\zeta_{15})^+\)	$4$	$[4, 0]$	89.3	\( 89 \)	\( -89 \)	$5.25277$	$(-2a^3+a^2+7a-2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$3$	3B.1.2	$1$	\( 1 \)	$0.006414098$	$1474.084412$	1.127565233	\( -\frac{79441}{89} a^{3} - \frac{10986}{89} a^{2} + \frac{246723}{89} a + \frac{51251}{89} \)	\( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 2 a\) , \( 2 a^{3} + a^{2} - 6 a\) , \( 3 a^{3} + a^{2} - 9 a - 2\bigr] \)	${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-2\right){x}^{2}+\left(2a^{3}+a^{2}-6a\right){x}+3a^{3}+a^{2}-9a-2$

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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.