Cremona's table of elliptic curves

10192 = 2⁴ · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 7+ 13-	Signs for the Atkin-Lehner involutions
Class	10192p	Isogeny class
Conductor	10192	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	6492304 = 24 · 74 · 132	Discriminant
Eigenvalues	2- -1 -3 7+ -3 13-  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-702,-6929]	[a1,a2,a3,a4,a6]
Generators	[-15:1:1]	Generators of the group modulo torsion
j	997335808/169	j-invariant
L	2.4399968378704	L(r)(E,1)/r!
Ω	0.92740226115315	Real period
R	1.3155008026595	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	2548c1 40768by1 91728dq1 10192t1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192p1

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	-3	+	-3	-	3	-5	9	-6	1	-7	6	-8	3	-9	9	11	13	0	-7	1	12	-3	2

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Quadratic twists for elliptic curve 10192p1

-4	8	-3	-7
2548c1	40768by1	91728dq1	10192t1

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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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