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	7488q	Isogeny class
Conductor	7488	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8384643072 = 215 · 39 · 13	Discriminant
Eigenvalues	2+ 3- -2  0  4 13+  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-134796,19048624]	[a1,a2,a3,a4,a6]
j	11339065490696/351	j-invariant
L	1.9191931100219	L(r)(E,1)/r!
Ω	0.95959655501095	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	7488r3 3744h3 2496h3 97344bq4	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488q3

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

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Quadratic twists for elliptic curve 7488q3

-4	8	-3	13
7488r3	3744h3	2496h3	97344bq4

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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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