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	16	Product of Tamagawa factors cp
Δ	54500179968 = 214 · 39 · 132	Discriminant
Eigenvalues	2- 3-  0 -2  0 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5340,149776]	[a1,a2,a3,a4,a6]
Generators	[5:351:1]	Generators of the group modulo torsion
j	1409938000/4563	j-invariant
L	3.9687489207225	L(r)(E,1)/r!
Ω	1.1236214380519	Real period
R	0.88302625473296	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	7488k2 1872p2 2496ba2 97344en2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488bp2

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 7488bp2

-4	8	-3	13
7488k2	1872p2	2496ba2	97344en2

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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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