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
24.1-a5	24.1-a	$6$	$8$	\(\Q(\sqrt{15}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$1.53203$	$(2,a+1), (3,a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$1$	$37.20447790$	1.200769361	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \)	${y}^2={x}^{3}-{x}^{2}-64{x}+220$
24.1-b5	24.1-b	$6$	$8$	\(\Q(\sqrt{15}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \)	$1.53203$	$(2,a+1), (3,a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$1$	$37.20447790$	2.401538722	\( \frac{28756228}{3} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -131 a - 500\) , \( 1474 a + 5714\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-131a-500\right){x}+1474a+5714$
24.1-c5	24.1-c	$6$	$8$	\(\Q(\sqrt{15}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{2} \)	$1.53203$	$(2,a+1), (3,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$1.665930347$	$5.683508517$	2.444712118	\( \frac{28756228}{3} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -220\bigr] \)	${y}^2={x}^{3}+{x}^{2}-64{x}-220$
24.1-d5	24.1-d	$6$	$8$	\(\Q(\sqrt{15}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{2} \)	$1.53203$	$(2,a+1), (3,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$0.748483442$	$5.683508517$	2.196762362	\( \frac{28756228}{3} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -127 a - 489\) , \( -1860 a - 7203\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-127a-489\right){x}-1860a-7203$

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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.