Cremona's table of elliptic curves

1265 = 5 · 11 · 23

Field	Data	Notes
Atkin-Lehner	5- 11+ 23-	Signs for the Atkin-Lehner involutions
Class	1265a	Isogeny class
Conductor	1265	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	136	Modular degree for the optimal curve
Δ	-13915 = -1 · 5 · 112 · 23	Discriminant
Eigenvalues	-2 -2 5-  3 11+  0 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,0,-6]	[a1,a2,a3,a4,a6]
Generators	[3:5:1]	Generators of the group modulo torsion
j	-4096/13915	j-invariant
L	1.1537896860042	L(r)(E,1)/r!
Ω	1.7989073158259	Real period
R	0.32069180992642	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20240x1 80960n1 11385h1 6325a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1265a1

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
-2	-2	-	3	+	0	-3	-6	-	9	-9	-1	-5	4	8	-5	-1	-4	-11	-3	4	-10	7	12	2

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Quadratic twists for elliptic curve 1265a1

-4	8	-3	5	-7	-11	-23
20240x1	80960n1	11385h1	6325a1	61985g1	13915l1	29095c1

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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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