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	3120p	Isogeny class
Conductor	3120	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-449280 = -1 · 28 · 33 · 5 · 13	Discriminant
Eigenvalues	2- 3+ 5+  1 -3 13-  3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,19,-15]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	2809856/1755	j-invariant
L	2.7801909362429	L(r)(E,1)/r!
Ω	1.7100634337716	Real period
R	0.81289117156053	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	780d1 12480cw1 9360ca1 15600cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3120p1

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
-	+	+	1	-3	-	3	-2	-3	6	-2	-7	9	-8	6	3	0	-7	4	-3	-10	1	0	3	-1

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Quadratic twists for elliptic curve 3120p1

-4	8	-3	5	13
780d1	12480cw1	9360ca1	15600cb1	40560bo1

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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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