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	7504i	Isogeny class
Conductor	7504	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	80878779856 = 24 · 75 · 673	Discriminant
Eigenvalues	2+  3 -1 7-  4  5  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1258,10379]	[a1,a2,a3,a4,a6]
j	13760862418944/5054923741	j-invariant
L	4.9529290719854	L(r)(E,1)/r!
Ω	0.99058581439709	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3752k1 30016cc1 67536u1 52528q1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7504i1

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	-1	-	4	5	0	4	3	9	1	1	-7	-8	-10	6	-6	6	+	-1	-14	-10	-14	-12	-18

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Quadratic twists for elliptic curve 7504i1

-4	8	-3	-7
3752k1	30016cc1	67536u1	52528q1

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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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