Cremona's table of elliptic curves

2990 = 2 · 5 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 5- 13+ 23+	Signs for the Atkin-Lehner involutions
Class	2990g	Isogeny class
Conductor	2990	Conductor
∏ cp	50	Product of Tamagawa factors cp
deg	3200	Modular degree for the optimal curve
Δ	956800000 = 210 · 55 · 13 · 23	Discriminant
Eigenvalues	2- -3 5- -1 -4 13+  7 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-252,-321]	[a1,a2,a3,a4,a6]
Generators	[-3:21:1]	Generators of the group modulo torsion
j	1763228727441/956800000	j-invariant
L	3.139367084256	L(r)(E,1)/r!
Ω	1.278140584387	Real period
R	0.049123971534973	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	23920s1 95680j1 26910m1 14950o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2990g1

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
-	-3	-	-1	-4	+	7	-2	+	-7	3	-8	6	4	2	2	-15	10	-9	0	13	1	-3	-11	-12

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Quadratic twists for elliptic curve 2990g1

-4	8	-3	5	13	-23
23920s1	95680j1	26910m1	14950o1	38870f1	68770n1

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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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