Cremona's table of elliptic curves

7488 = 2⁶ · 3² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+	Signs for the Atkin-Lehner involutions
Class	7488q	Isogeny class
Conductor	7488	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	35978634432 = 26 · 39 · 134	Discriminant
Eigenvalues	2+ 3- -2  0  4 13+  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-831,-1316]	[a1,a2,a3,a4,a6]
j	1360251712/771147	j-invariant
L	1.9191931100219	L(r)(E,1)/r!
Ω	0.95959655501095	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	7488r1 3744h2 2496h1 97344bq1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488q1

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	0	4	+	6	8	-8	2	8	10	-6	4	0	-14	-12	10	8	0	-14	-4	4	10	10

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Quadratic twists for elliptic curve 7488q1

-4	8	-3	13
7488r1	3744h2	2496h1	97344bq1

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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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