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	1240d	Isogeny class
Conductor	1240	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	1922000 = 24 · 53 · 312	Discriminant
Eigenvalues	2-  2 5+ -4  4  4  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-31,0]	[a1,a2,a3,a4,a6]
j	212629504/120125	j-invariant
L	2.1747560408699	L(r)(E,1)/r!
Ω	2.1747560408699	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2480d1 9920k1 11160h1 6200c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1240d1

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
-	2	+	-4	4	4	4	4	2	2	+	8	-6	10	0	0	4	2	8	-16	0	-16	18	6	-10

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Quadratic twists for elliptic curve 1240d1

-4	8	-3	5	-7	-31
2480d1	9920k1	11160h1	6200c1	60760ba1	38440j1

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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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