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	7488z	Isogeny class
Conductor	7488	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	43041517129728 = 212 · 314 · 133	Discriminant
Eigenvalues	2+ 3-  2  2 -2 13- -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-104484,12995552]	[a1,a2,a3,a4,a6]
Generators	[181:117:1]	Generators of the group modulo torsion
j	42246001231552/14414517	j-invariant
L	4.9455608383106	L(r)(E,1)/r!
Ω	0.6293269104621	Real period
R	1.3097487585795	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	7488ba2 3744l1 2496f2 97344cf2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 7488z2

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

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Quadratic twists for elliptic curve 7488z2

-4	8	-3	13
7488ba2	3744l1	2496f2	97344cf2

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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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