Cremona's table of elliptic curves

265 = 5 · 53

Field	Data	Notes
Atkin-Lehner	5+ 53+	Signs for the Atkin-Lehner involutions
Class	265a	Isogeny class
Conductor	265	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	30	Modular degree for the optimal curve
Δ	6625 = 53 · 53	Discriminant
Eigenvalues	-1  0 5+  2  0 -6 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-138,656]	[a1,a2,a3,a4,a6]
Generators	[6:1:1]	Generators of the group modulo torsion
j	288673724529/6625	j-invariant
L	1.0720624179337	L(r)(E,1)/r!
Ω	3.9017641877433	Real period
R	1.099054034379	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	4240b1 16960g1 2385g1 1325b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 265a1

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	+	2	0	-6	-6	-2	-8	2	10	2	-6	-2	-2	+	4	10	0	-2	14	-10	8	-2	10

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Quadratic twists for elliptic curve 265a1

-4	8	-3	5	-7	-11	13	17	-19	53
4240b1	16960g1	2385g1	1325b1	12985c1	32065a1	44785e1	76585c1	95665a1	14045c1

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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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