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	4	Product of Tamagawa factors cp
Δ	-43890625 = -1 · 56 · 532	Discriminant
Eigenvalues	-1  0 5+  2  0 -6 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-133,702]	[a1,a2,a3,a4,a6]
Generators	[0:26:1]	Generators of the group modulo torsion
j	-258353141409/43890625	j-invariant
L	1.0720624179337	L(r)(E,1)/r!
Ω	1.9508820938717	Real period
R	0.54952701718949	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	4240b2 16960g2 2385g2 1325b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 265a2

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 265a2

-4	8	-3	5	-7	-11	13	17	-19	53
4240b2	16960g2	2385g2	1325b2	12985c2	32065a2	44785e2	76585c2	95665a2	14045c2

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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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