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
144.3-a1	144.3-a	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	144.3	\( 2^{4} \cdot 3^{2} \)	\( - 2^{8} \cdot 3^{3} \)	$1.11609$	$(-a+1), (2)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B.1.1	$1$	\( 2 \cdot 3 \)	$1$	$17.49341010$	0.808633167	\( 256 a + 1280 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a + 5\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+5\right){x}$
144.3-c1	144.3-c	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	144.3	\( 2^{4} \cdot 3^{2} \)	\( - 2^{8} \cdot 3^{9} \)	$1.11609$	$(-a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$12.34378250$	1.711774644	\( 256 a + 1280 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 11\) , \( 2 a + 2\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-11\right){x}+2a+2$
1296.1-b1	1296.1-b	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	1296.1	\( 2^{4} \cdot 3^{4} \)	\( - 2^{8} \cdot 3^{15} \)	$1.93313$	$(-a), (-a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B.1.2	$1$	\( 2^{2} \cdot 3 \)	$0.284723118$	$6.616599577$	3.134997205	\( 256 a + 1280 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a + 33\) , \( -37 a + 85\bigr] \)	${y}^2={x}^{3}+\left(-15a+33\right){x}-37a+85$
1296.1-g1	1296.1-g	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	1296.1	\( 2^{4} \cdot 3^{4} \)	\( - 2^{8} \cdot 3^{9} \)	$1.93313$	$(-a), (-a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$0.578818386$	$9.376938535$	3.010659962	\( 256 a + 1280 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 6\) , \( 3 a - 7\bigr] \)	${y}^2={x}^{3}+\left(-3a+6\right){x}+3a-7$

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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.