Cremona's table of elliptic curves

3120 = 2⁴ · 3 · 5 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13-	Signs for the Atkin-Lehner involutions
Class	3120q	Isogeny class
Conductor	3120	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	44483871744000 = 213 · 32 · 53 · 136	Discriminant
Eigenvalues	2- 3+ 5+ -2  0 13-  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-19136,973440]	[a1,a2,a3,a4,a6]
Generators	[-104:1352:1]	Generators of the group modulo torsion
j	189208196468929/10860320250	j-invariant
L	2.5949853948626	L(r)(E,1)/r!
Ω	0.63026761251492	Real period
R	0.34310629105997	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	390c4 12480cy4 9360cb4 15600cc4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3120q4

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

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Quadratic twists for elliptic curve 3120q4

-4	8	-3	5	13
390c4	12480cy4	9360cb4	15600cc4	40560br4

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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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