Cremona's table of elliptic curves

1240 = 2³ · 5 · 31

Field	Data	Notes
Atkin-Lehner	2- 5- 31+	Signs for the Atkin-Lehner involutions
Class	1240f	Isogeny class
Conductor	1240	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-992000 = -1 · 28 · 53 · 31	Discriminant
Eigenvalues	2- -1 5-  2 -2 -2 -5  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-25,77]	[a1,a2,a3,a4,a6]
Generators	[-1:10:1]	Generators of the group modulo torsion
j	-7023616/3875	j-invariant
L	2.4001381443606	L(r)(E,1)/r!
Ω	2.5810104908228	Real period
R	0.15498698106127	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2480f1 9920c1 11160d1 6200a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1240f1

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	-	2	-2	-2	-5	1	-4	-4	+	-1	-3	1	6	-9	1	-4	8	-13	-3	-4	-3	-6	-10

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Quadratic twists for elliptic curve 1240f1

-4	8	-3	5	-7	-31
2480f1	9920c1	11160d1	6200a1	60760t1	38440l1

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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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