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	7488bw	Isogeny class
Conductor	7488	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	6055575552 = 214 · 37 · 132	Discriminant
Eigenvalues	2- 3- -4  2  4 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-732,-6640]	[a1,a2,a3,a4,a6]
Generators	[-11:9:1]	Generators of the group modulo torsion
j	3631696/507	j-invariant
L	3.4794734622182	L(r)(E,1)/r!
Ω	0.92636443750657	Real period
R	1.8780262504375	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	7488u2 1872t2 2496v2 97344gc2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488bw2

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

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Quadratic twists for elliptic curve 7488bw2

-4	8	-3	13
7488u2	1872t2	2496v2	97344gc2

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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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