Cremona's table of elliptic curves

665 = 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	5- 7- 19+	Signs for the Atkin-Lehner involutions
Class	665c	Isogeny class
Conductor	665	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-665 = -1 · 5 · 7 · 19	Discriminant
Eigenvalues	1 -1 5- 7-  0 -4 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	-1771561/665	j-invariant
L	2.3451929413417	L(r)(E,1)/r!
Ω	4.8049229586084	Real period
R	0.48808127862698	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	10640x1 42560u1 5985k1 3325b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 665c1

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	-1	-	-	0	-4	-3	+	1	-10	-8	3	1	-11	-4	-5	14	8	-6	-5	15	-12	4	-14	14

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Quadratic twists for elliptic curve 665c1

-4	8	-3	5	-7	-11	13	-19
10640x1	42560u1	5985k1	3325b1	4655j1	80465m1	112385f1	12635f1

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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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