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
56.1-a2	56.1-a	$6$	$18$	\(\Q(\zeta_{28})^+\)	$6$	$[6, 0]$	56.1	\( 2^{3} \cdot 7 \)	\( 2^{12} \cdot 7^{6} \)	$129.61521$	$(a^5-5a^3+5a), (-a^4+a^3+4a^2-3a-2)$	$1$	$\Z/18\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	\( 2^{2} \cdot 3 \)	$0.389689685$	$44104.62610$	3.68261	\( -\frac{15625}{28} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}$
56.1-b2	56.1-b	$6$	$18$	\(\Q(\zeta_{28})^+\)	$6$	$[6, 0]$	56.1	\( 2^{3} \cdot 7 \)	\( 2^{12} \cdot 7^{6} \)	$129.61521$	$(a^5-5a^3+5a), (-a^4+a^3+4a^2-3a-2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1$	$347.0892353$	0.334661	\( -\frac{15625}{28} \)	\( \bigl[a^{5} - 4 a^{3} + 3 a\) , \( -a^{4} + 3 a^{2} + 1\) , \( 0\) , \( 2\) , \( 0\bigr] \)	${y}^2+\left(a^{5}-4a^{3}+3a\right){x}{y}={x}^{3}+\left(-a^{4}+3a^{2}+1\right){x}^{2}+2{x}$

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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.