Elliptic curve search results

Results (4 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
125.6-b2	125.6-b	$4$	$10$	3.3.169.1	$3$	$[3, 0]$	125.6	\( 5^{3} \)	\( 5^{14} \)	$2.59757$	$(-a^2+2a+3), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	\( 2 \)	$1$	$22.00024918$	0.846163430	\( -\frac{2843862}{3125} a^{2} + \frac{4771131}{3125} a + \frac{12367976}{3125} \)	\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 2\) , \( a^{2} - 2\) , \( 5 a^{2} - 8 a - 20\) , \( 14 a^{2} - 19 a - 53\bigr] \)	${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(5a^{2}-8a-20\right){x}+14a^{2}-19a-53$
125.6-c2	125.6-c	$4$	$10$	3.3.169.1	$3$	$[3, 0]$	125.6	\( 5^{3} \)	\( 5^{8} \)	$2.59757$	$(-a^2+2a+3), (-a+1)$	$1$	$\Z/10\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.1.1	$1$	\( 2 \cdot 5 \)	$0.752165662$	$90.63000163$	1.573125580	\( -\frac{2843862}{3125} a^{2} + \frac{4771131}{3125} a + \frac{12367976}{3125} \)	\( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 3\) , \( a^{2} - 3\) , \( 5 a^{2} - 7 a - 18\) , \( -4 a^{2} + 4 a + 13\bigr] \)	${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(5a^{2}-7a-18\right){x}-4a^{2}+4a+13$
625.2-k4	625.2-k	$4$	$10$	3.3.169.1	$3$	$[3, 0]$	625.2	\( 5^{4} \)	\( 5^{14} \)	$3.39674$	$(-a^2+2a+3), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	\( 2^{2} \)	$1$	$34.65821666$	2.666016666	\( -\frac{2843862}{3125} a^{2} + \frac{4771131}{3125} a + \frac{12367976}{3125} \)	\( \bigl[a^{2} - 2\) , \( a\) , \( a\) , \( 23 a^{2} - 24 a - 76\) , \( 54 a^{2} - 61 a - 187\bigr] \)	${y}^2+\left(a^{2}-2\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(23a^{2}-24a-76\right){x}+54a^{2}-61a-187$
625.2-s4	625.2-s	$4$	$10$	3.3.169.1	$3$	$[3, 0]$	625.2	\( 5^{4} \)	\( 5^{20} \)	$3.39674$	$(-a^2+2a+3), (-a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2, 5$	2B, 5B.4.1	$1$	\( 2^{3} \)	$1$	$13.24055067$	2.037007796	\( -\frac{2843862}{3125} a^{2} + \frac{4771131}{3125} a + \frac{12367976}{3125} \)	\( \bigl[a\) , \( -a^{2} + 2\) , \( a^{2} - 2\) , \( 34 a^{2} - 43 a - 123\) , \( -76 a^{2} + 94 a + 273\bigr] \)	${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(34a^{2}-43a-123\right){x}-76a^{2}+94a+273$

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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.