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	7488bp	Isogeny class
Conductor	7488	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	7074542592 = 210 · 312 · 13	Discriminant
Eigenvalues	2- 3-  0 -2  0 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-480,88]	[a1,a2,a3,a4,a6]
Generators	[26:72:1]	Generators of the group modulo torsion
j	16384000/9477	j-invariant
L	3.9687489207225	L(r)(E,1)/r!
Ω	1.1236214380519	Real period
R	1.7660525094659	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7488k1 1872p1 2496ba1 97344en1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488bp1

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

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Quadratic twists for elliptic curve 7488bp1

-4	8	-3	13
7488k1	1872p1	2496ba1	97344en1

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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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