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	6	Product of Tamagawa factors cp
Δ	185426694544 = 24 · 74 · 136	Discriminant
Eigenvalues	2- -1 -3 7+ -3 13-  3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1682,17179]	[a1,a2,a3,a4,a6]
Generators	[-7:169:1]	Generators of the group modulo torsion
j	13707167488/4826809	j-invariant
L	2.4399968378704	L(r)(E,1)/r!
Ω	0.92740226115315	Real period
R	0.43850026755317	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	2548c2 40768by2 91728dq2 10192t2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192p2

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 10192p2

-4	8	-3	-7
2548c2	40768by2	91728dq2	10192t2

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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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