Cremona's table of elliptic curves

13260 = 2² · 3 · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13+ 17-	Signs for the Atkin-Lehner involutions
Class	13260d	Isogeny class
Conductor	13260	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	41472	Modular degree for the optimal curve
Δ	28240955730000 = 24 · 32 · 54 · 13 · 176	Discriminant
Eigenvalues	2- 3+ 5+  0 -6 13+ 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7621,-11954]	[a1,a2,a3,a4,a6]
Generators	[-69:425:1]	Generators of the group modulo torsion
j	3059825077387264/1765059733125	j-invariant
L	3.1270996910736	L(r)(E,1)/r!
Ω	0.55719046433761	Real period
R	0.31179241522327	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	53040ch1 39780s1 66300z1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 13260d1

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
-	+	+	0	-6	+	-	-6	8	2	0	12	-10	8	-12	6	12	6	-2	-2	4	0	16	0	8

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Quadratic twists for elliptic curve 13260d1

-4	-3	5
53040ch1	39780s1	66300z1

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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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