Cremona's table of elliptic curves

4655 = 5 · 7² · 19

Field	Data	Notes
Atkin-Lehner	5+ 7+ 19-	Signs for the Atkin-Lehner involutions
Class	4655c	Isogeny class
Conductor	4655	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	6048	Modular degree for the optimal curve
Δ	-2738280475 = -1 · 52 · 78 · 19	Discriminant
Eigenvalues	0 -2 5+ 7+ -3 -4  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-13491,598665]	[a1,a2,a3,a4,a6]
Generators	[-131:367:1] [-33:1004:1]	Generators of the group modulo torsion
j	-47109013504/475	j-invariant
L	2.9647897307256	L(r)(E,1)/r!
Ω	1.2981253961364	Real period
R	3.4258513155372	Regulator
r	2	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	74480v1 41895bg1 23275c1 4655p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4655c1

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	-2	+	+	-3	-4	3	-	-9	0	-10	-10	-6	-4	-3	-12	0	-1	-10	0	11	-4	-3	0	2

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Quadratic twists for elliptic curve 4655c1

-4	-3	5	-7	-19
74480v1	41895bg1	23275c1	4655p1	88445d1

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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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