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	665a	Isogeny class
Conductor	665	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-39916625 = -1 · 53 · 75 · 19	Discriminant
Eigenvalues	-1 -1 5+ 7-  4  0 -1 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,64,258]	[a1,a2,a3,a4,a6]
Generators	[4:22:1]	Generators of the group modulo torsion
j	28962726911/39916625	j-invariant
L	1.2423862408178	L(r)(E,1)/r!
Ω	1.3794131389652	Real period
R	0.18013258040298	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	10640i1 42560bk1 5985s1 3325d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 665a1

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	+	-	4	0	-1	-	-3	-6	0	-11	5	-7	-8	-3	2	-8	2	1	-11	-12	0	10	-2

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Quadratic twists for elliptic curve 665a1

-4	8	-3	5	-7	-11	13	-19
10640i1	42560bk1	5985s1	3325d1	4655q1	80465c1	112385j1	12635b1

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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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