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-a4	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	\( -194645795136 a^{2} + 134089931040 a + 625653842512 \)	\( \bigl[a + 1\) , \( -a^{2} + 2\) , \( a^{2} - a - 1\) , \( -41518 a^{2} - 48578 a + 19134\) , \( -8607796 a^{2} - 10071865 a + 3966568\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-41518a^{2}-48578a+19134\right){x}-8607796a^{2}-10071865a+3966568$
25.2-b4	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	\( -194645795136 a^{2} + 134089931040 a + 625653842512 \)	\( \bigl[a + 1\) , \( a^{2} - 2 a - 1\) , \( a^{2} - 2\) , \( -5312850765 a^{2} - 6216494888 a + 2448220752\) , \( -394174470602711 a^{2} - 461218221425205 a + 181639982107606\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2a-1\right){x}^{2}+\left(-5312850765a^{2}-6216494888a+2448220752\right){x}-394174470602711a^{2}-461218221425205a+181639982107606$
400.2-b1	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	\( -194645795136 a^{2} + 134089931040 a + 625653842512 \)	\( \bigl[a^{2} - 1\) , \( -a^{2} + 3\) , \( a^{2} - 1\) , \( -19 a^{2} - 16 a - 28\) , \( 53 a^{2} + 166 a - 6\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-19a^{2}-16a-28\right){x}+53a^{2}+166a-6$
400.2-g1	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	\( -194645795136 a^{2} + 134089931040 a + 625653842512 \)	\( \bigl[a^{2} - 1\) , \( -1\) , \( a^{2} - 1\) , \( -45 a^{2} - 46 a + 16\) , \( 254 a^{2} + 284 a - 114\bigr] \)	${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}-{x}^{2}+\left(-45a^{2}-46a+16\right){x}+254a^{2}+284a-114$

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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.