Cremona's table of elliptic curves

7504 = 2⁴ · 7 · 67

Field	Data	Notes
Atkin-Lehner	2+ 7- 67+	Signs for the Atkin-Lehner involutions
Class	7504l	Isogeny class
Conductor	7504	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	23532544 = 210 · 73 · 67	Discriminant
Eigenvalues	2+ -3 -3 7- -2 -5  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-139,586]	[a1,a2,a3,a4,a6]
Generators	[-11:28:1] [-5:34:1]	Generators of the group modulo torsion
j	290046852/22981	j-invariant
L	3.2129826034427	L(r)(E,1)/r!
Ω	2.0863638123961	Real period
R	0.12833262765391	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3752c1 30016bz1 67536v1 52528o1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7504l1

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
+	-3	-3	-	-2	-5	2	-6	-1	-1	-7	3	-3	-2	0	2	-12	2	+	-9	10	-8	-6	-6	-14

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Quadratic twists for elliptic curve 7504l1

-4	8	-3	-7
3752c1	30016bz1	67536v1	52528o1

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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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