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	7488b	Isogeny class
Conductor	7488	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-13625044992 = -1 · 212 · 39 · 132	Discriminant
Eigenvalues	2+ 3+  2  0 -2 13+  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-324,-6048]	[a1,a2,a3,a4,a6]
Generators	[996:31428:1]	Generators of the group modulo torsion
j	-46656/169	j-invariant
L	4.7197227433409	L(r)(E,1)/r!
Ω	0.51577029712746	Real period
R	4.5754115442738	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	7488a2 3744b1 7488c2 97344n2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488b2

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 7488b2

-4	8	-3	13
7488a2	3744b1	7488c2	97344n2

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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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