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
3872.14-a4	3872.14-a	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	3872.14	\( 2^{5} \cdot 11^{2} \)	\( 2^{17} \cdot 11^{2} \)	$1.86497$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$0.584511757$	$2.457844850$	2.171994331	\( \frac{34643161}{176} a - \frac{7276683}{176} \)	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2 a + 22\) , \( 26 a - 14\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a+22\right){x}+26a-14$
3872.5-a4	3872.5-a	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	3872.5	\( 2^{5} \cdot 11^{2} \)	\( 2^{17} \cdot 11^{2} \)	$1.86497$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$0.584511757$	$2.457844850$	2.171994331	\( \frac{34643161}{176} a - \frac{7276683}{176} \)	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -3 a - 19\) , \( -a + 31\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3a-19\right){x}-a+31$
5324.6-b4	5324.6-b	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	5324.6	\( 2^{2} \cdot 11^{3} \)	\( 2^{5} \cdot 11^{8} \)	$2.01952$	$(a), (-a+1), (-2a+3), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$1.482136211$	2.240779327	\( \frac{34643161}{176} a - \frac{7276683}{176} \)	\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 9 a - 62\) , \( 51 a - 162\bigr] \)	${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-62\right){x}+51a-162$
5324.7-e4	5324.7-e	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	5324.7	\( 2^{2} \cdot 11^{3} \)	\( 2^{5} \cdot 11^{8} \)	$2.01952$	$(a), (-a+1), (-2a+3), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{3} \)	$1$	$1.482136211$	2.240779327	\( \frac{34643161}{176} a - \frac{7276683}{176} \)	\( \bigl[1\) , \( -a\) , \( 0\) , \( 16 a + 46\) , \( -130 a + 160\bigr] \)	${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(16a+46\right){x}-130a+160$
15488.20-f1	15488.20-f	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	15488.20	\( 2^{7} \cdot 11^{2} \)	\( 2^{23} \cdot 11^{2} \)	$2.63746$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$2.418339135$	$1.737958760$	6.354298938	\( \frac{34643161}{176} a - \frac{7276683}{176} \)	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -22 a - 22\) , \( 67 a + 11\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a-22\right){x}+67a+11$
15488.5-f1	15488.5-f	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	15488.5	\( 2^{7} \cdot 11^{2} \)	\( 2^{23} \cdot 11^{2} \)	$2.63746$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$2.418339135$	$1.737958760$	6.354298938	\( \frac{34643161}{176} a - \frac{7276683}{176} \)	\( \bigl[a\) , \( a\) , \( a\) , \( -16 a + 45\) , \( 73 a + 50\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-16a+45\right){x}+73a+50$
23716.5-o1	23716.5-o	$4$	$4$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	23716.5	\( 2^{2} \cdot 7^{2} \cdot 11^{2} \)	\( 2^{5} \cdot 7^{6} \cdot 11^{2} \)	$2.93392$	$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$1$	$1.857956067$	5.617931086	\( \frac{34643161}{176} a - \frac{7276683}{176} \)	\( \bigl[1\) , \( a\) , \( a\) , \( 28 a - 18\) , \( -47 a - 46\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(28a-18\right){x}-47a-46$

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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.