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-k1	9900.5-k	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	9900.5	\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \)	\( 2^{16} \cdot 3^{10} \cdot 5^{4} \cdot 11^{4} \)	$2.95627$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 2^{6} \)	$0.459521475$	$0.581459739$	5.155954704	\( \frac{3235796719033}{25404192000} a + \frac{20214965063}{8468064000} \)	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -22 a - 51\) , \( 407 a - 267\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-22a-51\right){x}+407a-267$
49500.6-v1	49500.6-v	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	49500.6	\( 2^{2} \cdot 3^{2} \cdot 5^{3} \cdot 11 \)	\( 2^{16} \cdot 3^{10} \cdot 5^{10} \cdot 11^{4} \)	$4.42065$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{9} \)	$0.805103324$	$0.260036700$	8.079786671	\( \frac{3235796719033}{25404192000} a + \frac{20214965063}{8468064000} \)	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -177 a + 295\) , \( -3624 a - 1707\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-177a+295\right){x}-3624a-1707$
49500.7-k1	49500.7-k	$4$	$4$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	49500.7	\( 2^{2} \cdot 3^{2} \cdot 5^{3} \cdot 11 \)	\( 2^{16} \cdot 3^{10} \cdot 5^{10} \cdot 11^{4} \)	$4.42065$	$(-a), (a-1), (-a-1), (a-2), (-2a+1), (2)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{11} \cdot 3 \)	$0.065495810$	$0.260036700$	7.887566617	\( \frac{3235796719033}{25404192000} a + \frac{20214965063}{8468064000} \)	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 198 a - 247\) , \( -3210 a + 6515\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(198a-247\right){x}-3210a+6515$

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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.