Cremona's table of elliptic curves

7442 = 2 · 61²

Field	Data	Notes
Atkin-Lehner	2- 61-	Signs for the Atkin-Lehner involutions
Class	7442c	Isogeny class
Conductor	7442	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	161040	Modular degree for the optimal curve
Δ	-748425349941385024 = -1 · 26 · 619	Discriminant
Eigenvalues	2-  2  3 -3 -3 -5 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-61474,-42059921]	[a1,a2,a3,a4,a6]
Generators	[2369043:133414847:729]	Generators of the group modulo torsion
j	-2197/64	j-invariant
L	8.6117546332944	L(r)(E,1)/r!
Ω	0.12360578374973	Real period
R	5.8059275033136	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	59536h1 66978i1 7442a1	Quadratic twists by: -4 -3 61

Hecke Eigenvalues for elliptic curve 7442c1

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	3	-3	-3	-5	-6	2	-9	-6	0	6	9	0	0	0	3	-	3	0	-7	15	-12	0	-10

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Quadratic twists for elliptic curve 7442c1

-4	-3	61
59536h1	66978i1	7442a1

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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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