Cremona's table of elliptic curves

65 = 5 · 13

Field	Data	Notes
Atkin-Lehner	5+ 13+	Signs for the Atkin-Lehner involutions
Class	65a	Isogeny class
Conductor	65	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	65 = 5 · 13	Discriminant
Eigenvalues	-1 -2 5+ -4  2 13+  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1,0]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	117649/65	j-invariant
L	0.50533434230686	L(r)(E,1)/r!
Ω	5.3828534705718	Real period
R	0.37551409866127	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	1040c1 4160g1 585h1 325c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 65a1

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	-2	+	-4	2	+	2	-6	-6	2	-10	-2	-6	10	4	2	6	2	-4	6	-6	-12	-16	2	-2

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Quadratic twists for elliptic curve 65a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43
1040c1	4160g1	585h1	325c1	3185i1	7865b1	845a1	18785c1	23465a1	34385i1	54665c1	62465h1	88985f1	109265e1	120185d1

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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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