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
deg	72	Modular degree for the optimal curve
Δ	39401 = 312 · 41	Discriminant
Eigenvalues	1  0  2  2 -4 -4 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-11,-8]	[a1,a2,a3,a4,a6]
Generators	[-18:19:8]	Generators of the group modulo torsion
j	154854153/39401	j-invariant
L	3.373951025244	L(r)(E,1)/r!
Ω	2.6593937085165	Real period
R	2.5373836257784	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	20336b1 81344g1 11439f1 31775h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1271a1

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 1271a1

-4	8	-3	5	-7	-31	41
20336b1	81344g1	11439f1	31775h1	62279a1	39401a1	52111c1

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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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