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	7488f	Isogeny class
Conductor	7488	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-1472200704 = -1 · 222 · 33 · 13	Discriminant
Eigenvalues	2+ 3+  2 -2  4 13-  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-204,2160]	[a1,a2,a3,a4,a6]
j	-132651/208	j-invariant
L	2.7136623649246	L(r)(E,1)/r!
Ω	1.3568311824623	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	7488bg1 234c1 7488h1 97344p1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488f1

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	-2	4	-	0	6	4	8	-2	-6	6	8	8	-12	-4	-10	2	-16	14	-4	12	-6	-10

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Quadratic twists for elliptic curve 7488f1

-4	8	-3	13
7488bg1	234c1	7488h1	97344p1

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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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