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
288.2-b2	288.2-b	$2$	$2$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{9} \)	$2.11468$	$(-a-2), (-a+3), (-2a+7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$0.356320913$	$8.764309677$	3.261769806	\( -3588 a + 16608 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( -435 a - 1032\) , \( 6573 a + 15593\bigr] \)	${y}^2={x}^{3}+\left(-435a-1032\right){x}+6573a+15593$
288.2-e2	288.2-e	$2$	$2$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	288.2	\( 2^{5} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{9} \)	$2.11468$	$(-a-2), (-a+3), (-2a+7)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$1$	$10.77160689$	1.875096078	\( -3588 a + 16608 \)	\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a - 72\) , \( -87 a + 293\bigr] \)	${y}^2={x}^{3}+\left(21a-72\right){x}-87a+293$
576.3-f2	576.3-f	$2$	$2$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	576.3	\( 2^{6} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{3} \)	$2.51479$	$(-a-2), (-a+3), (-2a+7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \)	$0.783037154$	$15.18022965$	4.138412119	\( -3588 a + 16608 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a - 5\) , \( 0\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-5\right){x}$
576.3-h2	576.3-h	$2$	$2$	\(\Q(\sqrt{33}) \)	$2$	$[2, 0]$	576.3	\( 2^{6} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{3} \)	$2.51479$	$(-a-2), (-a+3), (-2a+7)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$0.199074584$	$18.65697041$	3.879280844	\( -3588 a + 16608 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 326 a - 1093\) , \( -5364 a + 18092\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(326a-1093\right){x}-5364a+18092$

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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.