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
2028.1-a8	2028.1-a	$8$	$12$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	2028.1	\( 2^{2} \cdot 3 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{3} \cdot 13^{5} \)	$2.07729$	$(a+1), (a), (a+4), (a-4)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B.1.1	$1$	\( 2^{2} \cdot 3^{2} \)	$1$	$7.575150816$	2.186757681	\( \frac{7050642069267500}{257049} a + \frac{1356896696001000}{28561} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 72 a - 171\) , \( -2333 a + 4144\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(72a-171\right){x}-2333a+4144$
2028.1-h8	2028.1-h	$8$	$12$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	2028.1	\( 2^{2} \cdot 3 \cdot 13^{2} \)	\( - 2^{8} \cdot 3^{3} \cdot 13^{5} \)	$2.07729$	$(a+1), (a), (a+4), (a-4)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2, 3$	2B, 3B.1.2	$1$	\( 2^{2} \)	$5.325757738$	$0.936092452$	2.878322969	\( \frac{7050642069267500}{257049} a + \frac{1356896696001000}{28561} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 74 a - 168\) , \( 2406 a - 4314\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(74a-168\right){x}+2406a-4314$

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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.