Elliptic curve search results

Results (6 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
45.1-a2	45.1-a	$8$	$16$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	45.1	\( 3^{2} \cdot 5 \)	\( 3^{2} \cdot 5^{2} \)	$1.46377$	$(5,a), (3)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2 \)	$2.148891872$	$8.942806850$	1.519247123	\( -\frac{1}{15} \)	\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)	${y}^2+{x}{y}+{y}={x}^3+{x}^2$
45.1-b2	45.1-b	$8$	$16$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	45.1	\( 3^{2} \cdot 5 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)	$1.46377$	$(5,a), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	\( 2 \)	$1$	$8.942806850$	1.413981916	\( -\frac{1}{15} \)	\( \bigl[a\) , \( 0\) , \( 0\) , \( 2\) , \( -2\bigr] \)	${y}^2+a{x}{y}={x}^3+2{x}-2$
405.1-a2	405.1-a	$8$	$16$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	405.1	\( 3^{4} \cdot 5 \)	\( 2^{12} \cdot 3^{14} \cdot 5^{2} \)	$2.53532$	$(5,a), (3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$4$	\( 2^{3} \)	$1$	$2.980935616$	1.885309221	\( -\frac{1}{15} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 5\) , \( 43\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+5{x}+43$
405.1-b2	405.1-b	$8$	$16$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	405.1	\( 3^{4} \cdot 5 \)	\( 3^{14} \cdot 5^{2} \)	$2.53532$	$(5,a), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$1.259224764$	$2.980935616$	4.748056122	\( -\frac{1}{15} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \)	${y}^2+{x}{y}={x}^3-{x}^2-5$
720.1-c2	720.1-c	$8$	$16$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	720.1	\( 2^{4} \cdot 3^{2} \cdot 5 \)	\( 2^{12} \cdot 3^{2} \cdot 5^{2} \)	$2.92753$	$(2,a), (5,a), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$1$	$4.471403425$	2.827963832	\( -\frac{1}{15} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( 0\bigr] \)	${y}^2+a{x}{y}={x}^3-{x}^2+4{x}$
720.1-f2	720.1-f	$8$	$16$	\(\Q(\sqrt{-10}) \)	$2$	$[0, 1]$	720.1	\( 2^{4} \cdot 3^{2} \cdot 5 \)	\( 2^{24} \cdot 3^{2} \cdot 5^{2} \)	$2.92753$	$(2,a), (5,a), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{3} \)	$0.928726450$	$4.471403425$	5.252809626	\( -\frac{1}{15} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -12\bigr] \)	${y}^2={x}^3+{x}^2-12$

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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.