Cremona's table of elliptic curves

5655 = 3 · 5 · 13 · 29

Field	Data	Notes
Atkin-Lehner	3- 5- 13- 29-	Signs for the Atkin-Lehner involutions
Class	5655f	Isogeny class
Conductor	5655	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	-42154750755 = -1 · 33 · 5 · 135 · 292	Discriminant
Eigenvalues	0 3- 5-  1 -5 13- -3  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-20215,-1113074]	[a1,a2,a3,a4,a6]
Generators	[398:7351:1]	Generators of the group modulo torsion
j	-913621755765293056/42154750755	j-invariant
L	4.0879512387255	L(r)(E,1)/r!
Ω	0.20019265071525	Real period
R	0.68066954907684	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	90480bn1 16965g1 28275a1 73515f1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5655f1

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	-	-	1	-5	-	-3	0	1	-	4	-9	3	-6	12	-1	-4	7	-12	-11	-6	-1	2	5	-7

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Quadratic twists for elliptic curve 5655f1

-4	-3	5	13
90480bn1	16965g1	28275a1	73515f1

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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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