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	10192t	Isogeny class
Conductor	10192	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	21815265186407056 = 24 · 710 · 136	Discriminant
Eigenvalues	2-  1  3 7- -3 13+ -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-82434,-5727541]	[a1,a2,a3,a4,a6]
Generators	[66703395:626327351:185193]	Generators of the group modulo torsion
j	13707167488/4826809	j-invariant
L	6.0747148243886	L(r)(E,1)/r!
Ω	0.28992127940133	Real period
R	10.476490095747	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	2548f2 40768dq2 91728er2 10192p2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192t2

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 10192t2

-4	8	-3	-7
2548f2	40768dq2	91728er2	10192p2

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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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