Elliptic curve search results

Results (3 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
9900.5-k4	9900.5-k	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	9900.5	\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( 2^{4} \cdot 3^{16} \cdot 5^{13} \cdot 11 \)	$2.95627$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 2^{8} \)	$0.459521475$	$0.145364934$	5.155954704	\( -\frac{1087353359208666963341}{23493164062500} a + \frac{1889031412831645197491}{70479492187500} \)	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -482 a + 13049\) , \( 332735 a - 115039\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-482a+13049\right){x}+332735a-115039$
49500.6-v4	49500.6-v	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	49500.6	\( 2^{2} \cdot 3^{2} \cdot 5^{3} \cdot 11 \)	\( 2^{4} \cdot 3^{16} \cdot 5^{19} \cdot 11 \)	$4.42065$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{7} \)	$3.220413299$	$0.065009175$	8.079786671	\( -\frac{1087353359208666963341}{23493164062500} a + \frac{1889031412831645197491}{70479492187500} \)	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 38663 a - 21765\) , \( -2811068 a - 2821611\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(38663a-21765\right){x}-2811068a-2821611$
49500.7-k4	49500.7-k	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	49500.7	\( 2^{2} \cdot 3^{2} \cdot 5^{3} \cdot 11 \)	\( 2^{4} \cdot 3^{16} \cdot 5^{19} \cdot 11 \)	$4.42065$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{9} \cdot 3 \)	$0.261983241$	$0.065009175$	7.887566617	\( -\frac{1087353359208666963341}{23493164062500} a + \frac{1889031412831645197491}{70479492187500} \)	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -38182 a + 8713\) , \( -3238110 a + 4806815\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38182a+8713\right){x}-3238110a+4806815$

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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.