Cremona's table of elliptic curves

13286 = 2 · 7 · 13 · 73

Field	Data	Notes
Atkin-Lehner	2+ 7- 13+ 73+	Signs for the Atkin-Lehner involutions
Class	13286f	Isogeny class
Conductor	13286	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-9114196 = -1 · 22 · 74 · 13 · 73	Discriminant
Eigenvalues	2+ -2 -3 7-  0 13+  0 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-185,960]	[a1,a2,a3,a4,a6]
Generators	[-12:44:1] [9:-12:1]	Generators of the group modulo torsion
j	-694800198793/9114196	j-invariant
L	3.2073646456285	L(r)(E,1)/r!
Ω	2.3177636591713	Real period
R	0.17297733490526	Regulator
r	2	Rank of the group of rational points
S	0.99999999999958	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	106288m1 119574be1 93002j1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 13286f1

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	-3	-	0	+	0	-7	-2	-6	-2	-6	0	12	-6	-8	10	-9	-9	-7	+	-14	0	-12	4

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Quadratic twists for elliptic curve 13286f1

-4	-3	-7
106288m1	119574be1	93002j1

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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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