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	665d	Isogeny class
Conductor	665	Conductor
∏ cp	50	Product of Tamagawa factors cp
deg	600	Modular degree for the optimal curve
Δ	-18960396875 = -1 · 55 · 75 · 192	Discriminant
Eigenvalues	-2 -1 5- 7- -3 -1  3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-210,6798]	[a1,a2,a3,a4,a6]
Generators	[-18:66:1]	Generators of the group modulo torsion
j	-1029077364736/18960396875	j-invariant
L	1.0781458035896	L(r)(E,1)/r!
Ω	1.0294222183049	Real period
R	0.52366550110261	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	10640y1 42560v1 5985m1 3325c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 665d1

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	-1	-	-	-3	-1	3	+	4	5	-8	-12	-8	4	-7	4	-10	2	-12	-8	-6	-15	4	10	-7

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Quadratic twists for elliptic curve 665d1

-4	8	-3	5	-7	-11	13	-19
10640y1	42560v1	5985m1	3325c1	4655k1	80465o1	112385g1	12635h1

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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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