Elliptic curve search results

Results (5 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
25.3-a2	25.3-a	$4$	$4$	3.3.169.1	$3$	$[3, 0]$	25.3	\( 5^{2} \)	\( 5^{4} \)	$1.98642$	$(-a^2+2a+3), (-a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	\( 2^{2} \)	$1$	$52.25768563$	1.004955493	\( \frac{217317341}{5} a^{2} - \frac{2574843704}{25} a - \frac{785560232}{25} \)	\( \bigl[a\) , \( a^{2} - a - 4\) , \( a\) , \( -7 a^{2} + 2 a + 5\) , \( -12 a^{2} - 10 a - 3\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-7a^{2}+2a+5\right){x}-12a^{2}-10a-3$
125.3-d3	125.3-d	$4$	$4$	3.3.169.1	$3$	$[3, 0]$	125.3	\( 5^{3} \)	\( 5^{10} \)	$2.59757$	$(-a^2+2a+3), (-a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{3} \)	$1$	$30.06441151$	1.156323519	\( \frac{217317341}{5} a^{2} - \frac{2574843704}{25} a - \frac{785560232}{25} \)	\( \bigl[a^{2} - a - 2\) , \( 0\) , \( 1\) , \( -11 a^{2} + 6 a + 1\) , \( 52 a + 12\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+{y}={x}^{3}+\left(-11a^{2}+6a+1\right){x}+52a+12$
125.6-a2	125.6-a	$4$	$4$	3.3.169.1	$3$	$[3, 0]$	125.6	\( 5^{3} \)	\( 5^{10} \)	$2.59757$	$(-a^2+2a+3), (-a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{3} \)	$1$	$41.50034334$	1.596167051	\( \frac{217317341}{5} a^{2} - \frac{2574843704}{25} a - \frac{785560232}{25} \)	\( \bigl[a^{2} - a - 3\) , \( a - 1\) , \( a + 1\) , \( -20 a^{2} - 65 a - 50\) , \( -221 a^{2} - 440 a - 187\bigr] \)	${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a^{2}-65a-50\right){x}-221a^{2}-440a-187$
625.2-i3	625.2-i	$4$	$4$	3.3.169.1	$3$	$[3, 0]$	625.2	\( 5^{4} \)	\( 5^{16} \)	$3.39674$	$(-a^2+2a+3), (-a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{4} \)	$0.157322213$	$69.80113317$	2.534138954	\( \frac{217317341}{5} a^{2} - \frac{2574843704}{25} a - \frac{785560232}{25} \)	\( \bigl[a + 1\) , \( -1\) , \( a^{2} - a - 3\) , \( -48 a^{2} + 59 a + 17\) , \( 236 a^{2} - 331 a - 106\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}-{x}^{2}+\left(-48a^{2}+59a+17\right){x}+236a^{2}-331a-106$
625.5-e3	625.5-e	$4$	$4$	3.3.169.1	$3$	$[3, 0]$	625.5	\( 5^{4} \)	\( 5^{10} \)	$3.39674$	$(-a^2+2a+3), (-a^2+a+2), (-a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{4} \)	$0.072773617$	$156.0800786$	2.621195068	\( \frac{217317341}{5} a^{2} - \frac{2574843704}{25} a - \frac{785560232}{25} \)	\( \bigl[a^{2} - a - 2\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( -180 a^{2} + 433 a + 127\) , \( 1977 a^{2} - 4699 a - 1431\bigr] \)	${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-180a^{2}+433a+127\right){x}+1977a^{2}-4699a-1431$

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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.