Cremona's table of elliptic curves

9386 = 2 · 13 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 13+ 19+	Signs for the Atkin-Lehner involutions
Class	9386a	Isogeny class
Conductor	9386	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-2819103872 = -1 · 27 · 132 · 194	Discriminant
Eigenvalues	2+ -1  4  2  3 13+ -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-103253,12727405]	[a1,a2,a3,a4,a6]
Generators	[185:-90:1]	Generators of the group modulo torsion
j	-934165699635529/21632	j-invariant
L	3.7334856089386	L(r)(E,1)/r!
Ω	1.0380302618813	Real period
R	1.7983510433366	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	75088o1 84474bw1 122018w1 9386j1	Quadratic twists by: -4 -3 13 -19

Hecke Eigenvalues for elliptic curve 9386a1

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	4	2	3	+	-6	+	0	-8	-2	-8	-5	-4	-6	4	11	10	5	6	-11	-14	7	-10	-1

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Quadratic twists for elliptic curve 9386a1

-4	-3	13	-19
75088o1	84474bw1	122018w1	9386j1

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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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