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	1	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	665 = 5 · 7 · 19	Discriminant
Eigenvalues	1  0 5- 7+ -4 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-14,-17]	[a1,a2,a3,a4,a6]
Generators	[138:67:27]	Generators of the group modulo torsion
j	315821241/665	j-invariant
L	2.5513395946814	L(r)(E,1)/r!
Ω	2.4602431252193	Real period
R	4.1481097027011	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10640z1 42560a1 5985i1 3325g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 665b1

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 665b1

-4	8	-3	5	-7	-11	13	-19
10640z1	42560a1	5985i1	3325g1	4655d1	80465s1	112385i1	12635c1

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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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