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	4655f	Isogeny class
Conductor	4655	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-23275 = -1 · 52 · 72 · 19	Discriminant
Eigenvalues	-2  0 5+ 7- -3 -6 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,7,-2]	[a1,a2,a3,a4,a6]
Generators	[1:2:1] [4:9:1]	Generators of the group modulo torsion
j	774144/475	j-invariant
L	2.4331022509155	L(r)(E,1)/r!
Ω	2.1981737850546	Real period
R	0.55343719124015	Regulator
r	2	Rank of the group of rational points
S	0.9999999999995	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	74480bl1 41895bn1 23275o1 4655m1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4655f1

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
-2	0	+	-	-3	-6	-3	+	-1	-8	4	-10	-10	-4	-13	-6	6	-3	10	6	5	-14	11	0	16

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Quadratic twists for elliptic curve 4655f1

-4	-3	5	-7	-19
74480bl1	41895bn1	23275o1	4655m1	88445u1

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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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