Elliptic curve search results

Results (7 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
275.2-a4	275.2-a	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	275.2	\( 5^{2} \cdot 11 \)	\( 5^{8} \cdot 11^{2} \)	$1.20689$	$(-a-1), (a-2), (-2a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{5} \)	$0.352424167$	$1.770622110$	1.505168807	\( \frac{22930509321}{6875} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}-59{x}+190$
1375.2-a4	1375.2-a	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1375.2	\( 5^{3} \cdot 11 \)	\( 5^{14} \cdot 11^{2} \)	$1.80472$	$(-a-1), (a-2), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$1$	$0.791846280$	1.910005093	\( \frac{22930509321}{6875} \)	\( \bigl[a\) , \( -a\) , \( 0\) , \( -177 a + 118\) , \( 760 a - 2090\bigr] \)	${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-177a+118\right){x}+760a-2090$
1375.3-a4	1375.3-a	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	1375.3	\( 5^{3} \cdot 11 \)	\( 5^{14} \cdot 11^{2} \)	$1.80472$	$(-a-1), (a-2), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$1$	$0.791846280$	1.910005093	\( \frac{22930509321}{6875} \)	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 177 a - 59\) , \( -760 a - 1330\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(177a-59\right){x}-760a-1330$
6875.3-a4	6875.3-a	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	6875.3	\( 5^{4} \cdot 11 \)	\( 5^{20} \cdot 11^{2} \)	$2.69869$	$(-a-1), (a-2), (-2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{5} \)	$0.596122623$	$0.354124422$	2.036784674	\( \frac{22930509321}{6875} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1480\) , \( 22272\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-1480{x}+22272$
22275.8-a4	22275.8-a	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	22275.8	\( 3^{4} \cdot 5^{2} \cdot 11 \)	\( 3^{12} \cdot 5^{8} \cdot 11^{2} \)	$3.62067$	$(-a), (a-1), (-a-1), (a-2), (-2a+1)$	$2$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{5} \)	$0.496724502$	$0.590207370$	5.657230102	\( \frac{22930509321}{6875} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -533\) , \( -4598\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-533{x}-4598$
27225.2-b4	27225.2-b	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	27225.2	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 5^{8} \cdot 11^{8} \)	$3.80695$	$(-a), (-a-1), (a-2), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{5} \)	$1$	$0.308225746$	1.486936948	\( \frac{22930509321}{6875} \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 649 a - 1952\) , \( -16071 a + 29400\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(649a-1952\right){x}-16071a+29400$
27225.8-b4	27225.8-b	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	27225.8	\( 3^{2} \cdot 5^{2} \cdot 11^{2} \)	\( 3^{6} \cdot 5^{8} \cdot 11^{8} \)	$3.80695$	$(a-1), (-a-1), (a-2), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{5} \)	$1$	$0.308225746$	1.486936948	\( \frac{22930509321}{6875} \)	\( \bigl[a\) , \( -a\) , \( a\) , \( -651 a - 1301\) , \( 16070 a + 13330\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-651a-1301\right){x}+16070a+13330$

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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.