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	3120a	Isogeny class
Conductor	3120	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-58500000000000 = -1 · 211 · 32 · 512 · 13	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-216,-367920]	[a1,a2,a3,a4,a6]
Generators	[194:2618:1]	Generators of the group modulo torsion
j	-546718898/28564453125	j-invariant
L	2.7398327179869	L(r)(E,1)/r!
Ω	0.28565788760081	Real period
R	4.7956538868895	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	1560c4 12480db4 9360q4 15600r4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3120a4

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

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Quadratic twists for elliptic curve 3120a4

-4	8	-3	5	13
1560c4	12480db4	9360q4	15600r4	40560h3

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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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