Cremona's table of elliptic curves

1245 = 3 · 5 · 83

Field	Data	Notes
Atkin-Lehner	3+ 5+ 83-	Signs for the Atkin-Lehner involutions
Class	1245a	Isogeny class
Conductor	1245	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	155625 = 3 · 54 · 83	Discriminant
Eigenvalues	1 3+ 5+  0  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-13,-8]	[a1,a2,a3,a4,a6]
j	273359449/155625	j-invariant
L	1.3458213911721	L(r)(E,1)/r!
Ω	2.6916427823442	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	19920k1 79680v1 3735e1 6225e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1245a1

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	0	2	-2	-4	8	6	8	-2	2	0	0	10	0	14	8	8	-10	8	-	-10	-2

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Quadratic twists for elliptic curve 1245a1

-4	8	-3	5	-7	-83
19920k1	79680v1	3735e1	6225e1	61005u1	103335g1

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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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