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	665b	Isogeny class
Conductor	665	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	442225 = 52 · 72 · 192	Discriminant
Eigenvalues	1  0 5- 7+ -4 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-19,0]	[a1,a2,a3,a4,a6]
Generators	[16:52:1]	Generators of the group modulo torsion
j	781229961/442225	j-invariant
L	2.5513395946814	L(r)(E,1)/r!
Ω	2.4602431252193	Real period
R	2.0740548513505	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10640z2 42560a2 5985i2 3325g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 665b2

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	0	-	+	-4	-2	2	-	-8	6	-8	-6	6	4	8	-6	-12	-2	4	-12	-6	12	-4	-10	2

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Quadratic twists for elliptic curve 665b2

-4	8	-3	5	-7	-11	13	-19
10640z2	42560a2	5985i2	3325g2	4655d2	80465s2	112385i2	12635c2

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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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