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	7504n	Isogeny class
Conductor	7504	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	7684096 = 214 · 7 · 67	Discriminant
Eigenvalues	2- -1 -1 7+ -2 -7 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-56,112]	[a1,a2,a3,a4,a6]
Generators	[-6:14:1] [-4:16:1]	Generators of the group modulo torsion
j	4826809/1876	j-invariant
L	4.3728615864243	L(r)(E,1)/r!
Ω	2.1334036684327	Real period
R	0.51242782263015	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	938a1 30016bj1 67536bi1 52528z1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7504n1

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	-1	+	-2	-7	-2	2	-1	-5	-9	-9	3	6	-12	-10	8	-2	+	-9	-2	8	-2	2	-18

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Quadratic twists for elliptic curve 7504n1

-4	8	-3	-7
938a1	30016bj1	67536bi1	52528z1

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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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