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
25.2-a3	25.2-a	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	25.2	\( 5^{2} \)	\( 5^{9} \)	$1.85891$	$(a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 5$	2B, 5B.4.2	$1$	\( 2 \)	$1$	$37.43514264$	1.538574885	\( 491380736 a^{2} + 574509056 a - 227098624 \)	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -4 a^{2} + a\) , \( 95 a^{2} - 265 a + 73\bigr] \)	${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a^{2}+a\right){x}+95a^{2}-265a+73$
25.2-b2	25.2-b	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	25.2	\( 5^{2} \)	\( 5^{3} \)	$1.85891$	$(a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 5$	2B, 5B.1.2	$1$	\( 2 \)	$1$	$10.86073623$	0.446373509	\( 491380736 a^{2} + 574509056 a - 227098624 \)	\( \bigl[0\) , \( a^{2} - 2 a - 3\) , \( 1\) , \( -377381 a^{2} - 441567 a + 173905\) , \( -232144315 a^{2} - 271628927 a + 106974682\bigr] \)	${y}^2+{y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-377381a^{2}-441567a+173905\right){x}-232144315a^{2}-271628927a+106974682$
400.2-b3	400.2-b	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	400.2	\( 2^{4} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{9} \)	$2.95084$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 5$	2B, 5B.4.2	$1$	\( 2 \)	$1$	$36.68657131$	1.507808793	\( 491380736 a^{2} + 574509056 a - 227098624 \)	\( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( 14 a^{2} - 12 a - 50\) , \( -45 a^{2} + 62 a + 84\bigr] \)	${y}^2={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(14a^{2}-12a-50\right){x}-45a^{2}+62a+84$
400.2-g3	400.2-g	$4$	$10$	3.3.148.1	$3$	$[3, 0]$	400.2	\( 2^{4} \cdot 5^{2} \)	\( 2^{12} \cdot 5^{3} \)	$2.95084$	$(a^2-a-2), (a^2-a-1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 5$	2B, 5B.4.2	$1$	\( 2 \)	$1$	$33.74301905$	1.386829540	\( 491380736 a^{2} + 574509056 a - 227098624 \)	\( \bigl[0\) , \( a^{2} - 1\) , \( 0\) , \( -2 a^{2} - 4 a - 2\) , \( 6 a^{2} - 4 a - 1\bigr] \)	${y}^2={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(-2a^{2}-4a-2\right){x}+6a^{2}-4a-1$

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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.