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
6.1-c4	6.1-c	$6$	$8$	4.4.16609.1	$4$	$[4, 0]$	6.1	\( 2 \cdot 3 \)	\( 2^{2} \cdot 3^{8} \)	$14.40719$	$(-a^2-a+2), (a^2-a-3)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	\( 2^{4} \)	$0.037059618$	$1884.259355$	2.167354094	\( -\frac{97259155}{26244} a^{3} + \frac{20327771}{2916} a^{2} + \frac{14950541}{13122} a + \frac{319978897}{26244} \)	\( \bigl[a^{3} - 4 a\) , \( a^{3} - 2 a^{2} - 5 a + 7\) , \( 0\) , \( -a^{3} + 2 a^{2} + 5 a - 8\) , \( 0\bigr] \)	${y}^2+\left(a^{3}-4a\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-5a+7\right){x}^{2}+\left(-a^{3}+2a^{2}+5a-8\right){x}$
18.1-h5	18.1-h	$6$	$8$	4.4.16609.1	$4$	$[4, 0]$	18.1	\( 2 \cdot 3^{2} \)	\( 2^{2} \cdot 3^{14} \)	$16.52796$	$(-a^2-a+2), (a^2-a-3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{3} \)	$1$	$446.3692956$	1.731779422	\( -\frac{97259155}{26244} a^{3} + \frac{20327771}{2916} a^{2} + \frac{14950541}{13122} a + \frac{319978897}{26244} \)	\( \bigl[a^{3} - a^{2} - 3 a + 4\) , \( a^{3} - 3 a - 1\) , \( a\) , \( 3 a^{3} + 8 a^{2} - 7 a - 27\) , \( -6 a^{3} + 8 a^{2} + 45 a\bigr] \)	${y}^2+\left(a^{3}-a^{2}-3a+4\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(3a^{3}+8a^{2}-7a-27\right){x}-6a^{3}+8a^{2}+45a$
48.2-e1	48.2-e	$6$	$8$	4.4.16609.1	$4$	$[4, 0]$	48.2	\( 2^{4} \cdot 3 \)	\( 2^{14} \cdot 3^{8} \)	$18.68381$	$(-a^2-a+2), (a^2-a-3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{5} \)	$1$	$448.0708264$	1.738380853	\( -\frac{97259155}{26244} a^{3} + \frac{20327771}{2916} a^{2} + \frac{14950541}{13122} a + \frac{319978897}{26244} \)	\( \bigl[a^{2} + a - 4\) , \( -a^{2} - a + 3\) , \( a^{2} - 3\) , \( 522 a^{3} + 614 a^{2} - 2927 a - 3967\) , \( 14539 a^{3} + 17170 a^{2} - 81491 a - 110779\bigr] \)	${y}^2+\left(a^{2}+a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(522a^{3}+614a^{2}-2927a-3967\right){x}+14539a^{3}+17170a^{2}-81491a-110779$

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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.