Cremona's table of elliptic curves

1271 = 31 · 41

Field	Data	Notes
Atkin-Lehner	31- 41-	Signs for the Atkin-Lehner involutions
Class	1271a	Isogeny class
Conductor	1271	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	52111 = 31 · 412	Discriminant
Eigenvalues	1  0  2  2 -4 -4 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-166,-783]	[a1,a2,a3,a4,a6]
Generators	[3636:24627:64]	Generators of the group modulo torsion
j	507596683833/52111	j-invariant
L	3.373951025244	L(r)(E,1)/r!
Ω	1.3296968542583	Real period
R	5.0747672515568	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20336b2 81344g2 11439f2 31775h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1271a2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	0	2	2	-4	-4	-4	-2	0	0	-	2	-	4	-10	12	-8	2	-14	14	10	-16	-4	4	-10

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Quadratic twists for elliptic curve 1271a2

-4	8	-3	5	-7	-31	41
20336b2	81344g2	11439f2	31775h2	62279a2	39401a2	52111c2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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