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-a4	24.1-a	$6$	$8$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{8} \)	$2.16662$	$(2,a), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$2.158547729$	$9.301119475$	3.665525556	\( \frac{1556068}{81} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1070 a - 5854\) , \( -44886 a - 245854\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-1070a-5854\right){x}-44886a-245854$
24.1-b4	24.1-b	$6$	$8$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{20} \cdot 3^{8} \)	$2.16662$	$(2,a), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$2.841664688$	$9.301119475$	2.412778368	\( \frac{1556068}{81} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \)	${y}^2={x}^{3}-{x}^{2}-24{x}-36$
24.1-c4	24.1-c	$6$	$8$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{8} \)	$2.16662$	$(2,a), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{4} \)	$1.068541721$	$22.73403407$	4.435140305	\( \frac{1556068}{81} \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 262 a - 1432\) , \( -4084 a + 22370\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(262a-1432\right){x}-4084a+22370$
24.1-d4	24.1-d	$6$	$8$	\(\Q(\sqrt{30}) \)	$2$	$[2, 0]$	24.1	\( 2^{3} \cdot 3 \)	\( 2^{8} \cdot 3^{8} \)	$2.16662$	$(2,a), (3,a)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$1.665930347$	$22.73403407$	3.457345033	\( \frac{1556068}{81} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -7\) , \( -5\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-7{x}-5$

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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.