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	7488k	Isogeny class
Conductor	7488	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	7074542592 = 210 · 312 · 13	Discriminant
Eigenvalues	2+ 3-  0  2  0 13+  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-480,-88]	[a1,a2,a3,a4,a6]
j	16384000/9477	j-invariant
L	2.234388748701	L(r)(E,1)/r!
Ω	1.1171943743505	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	7488bp1 468d1 2496a1 97344y1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488k1

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 7488k1

-4	8	-3	13
7488bp1	468d1	2496a1	97344y1

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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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