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	7488a	Isogeny class
Conductor	7488	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	16376256 = 26 · 39 · 13	Discriminant
Eigenvalues	2+ 3+  2  0  2 13+  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-459,3780]	[a1,a2,a3,a4,a6]
Generators	[194:665:8]	Generators of the group modulo torsion
j	8489664/13	j-invariant
L	4.8281514523513	L(r)(E,1)/r!
Ω	2.1980163831694	Real period
R	4.3931896862292	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	7488b1 3744j2 7488d1 97344o1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488a1

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	2	+	0	-4	-4	-8	8	-2	-6	4	-6	-4	6	-2	-4	-6	-2	-16	2	-10	-2

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Quadratic twists for elliptic curve 7488a1

-4	8	-3	13
7488b1	3744j2	7488d1	97344o1

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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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