Elliptic curve search results

Results (4 matches)

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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
729.1-d1	729.1-d	$2$	$3$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	729.1	\( 3^{6} \)	\( - 3^{8} \)	$1.67414$	$(-a), (-a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3B	$1$	\( 1 \)	$0.354151165$	$14.41546786$	2.831885807	\( 13515 a + 16707 \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -5\) , \( a - 5\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-5{x}+a-5$
729.1-e1	729.1-e	$2$	$3$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	729.1	\( 3^{6} \)	\( - 3^{14} \)	$1.67414$	$(-a), (-a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3B.1.2	$1$	\( 1 \)	$1$	$4.860164952$	1.347967226	\( 13515 a + 16707 \)	\( \bigl[a\) , \( -a\) , \( 1\) , \( a - 6\) , \( 6 a - 15\bigr] \)	${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-6\right){x}+6a-15$
729.1-f1	729.1-f	$2$	$3$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	729.1	\( 3^{6} \)	\( - 3^{20} \)	$1.67414$	$(-a), (-a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3B	$1$	\( 1 \)	$1$	$6.546120139$	1.815567063	\( 13515 a + 16707 \)	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 11 a - 33\) , \( -66 a + 144\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(11a-33\right){x}-66a+144$
729.1-g1	729.1-g	$2$	$3$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	729.1	\( 3^{6} \)	\( - 3^{14} \)	$1.67414$	$(-a), (-a+1)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$3$	3B.1.1	$1$	\( 3^{2} \)	$0.227641124$	$19.41608679$	2.451719308	\( 13515 a + 16707 \)	\( \bigl[1\) , \( -1\) , \( a\) , \( 7 a - 18\) , \( -29 a + 66\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(7a-18\right){x}-29a+66$

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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.