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-a3	144.3-a	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	144.3	\( 2^{4} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{3} \)	$1.11609$	$(-a+1), (2)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B.1.1	$1$	\( 2 \cdot 3 \)	$1$	$17.49341010$	0.808633167	\( 208912 a + 275168 \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a - 20\) , \( 20 a - 44\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a-20\right){x}+20a-44$
144.3-c3	144.3-c	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	144.3	\( 2^{4} \cdot 3^{2} \)	\( 2^{16} \cdot 3^{9} \)	$1.11609$	$(-a+1), (2)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2 \)	$1$	$12.34378250$	1.711774644	\( 208912 a + 275168 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 46 a - 109\) , \( -191 a + 441\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(46a-109\right){x}-191a+441$
1296.1-b3	1296.1-b	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	1296.1	\( 2^{4} \cdot 3^{4} \)	\( 2^{16} \cdot 3^{15} \)	$1.93313$	$(-a), (-a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B.1.2	$1$	\( 2^{2} \cdot 3 \)	$0.569446236$	$3.308299788$	3.134997205	\( 208912 a + 275168 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 75 a - 192\) , \( -352 a + 778\bigr] \)	${y}^2={x}^{3}+\left(75a-192\right){x}-352a+778$
1296.1-g3	1296.1-g	$4$	$6$	\(\Q(\sqrt{13}) \)	$2$	$[2, 0]$	1296.1	\( 2^{4} \cdot 3^{4} \)	\( 2^{16} \cdot 3^{9} \)	$1.93313$	$(-a), (-a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 3$	2B, 3B	$1$	\( 2^{2} \)	$1.157636773$	$4.688469267$	3.010659962	\( 208912 a + 275168 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 39\) , \( 24 a - 70\bigr] \)	${y}^2={x}^{3}+\left(12a-39\right){x}+24a-70$

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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.