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
deg	24192	Modular degree for the optimal curve
Δ	763813073296 = 24 · 710 · 132	Discriminant
Eigenvalues	2-  1  3 7- -3 13+ -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-34414,2445463]	[a1,a2,a3,a4,a6]
Generators	[171:1261:1]	Generators of the group modulo torsion
j	997335808/169	j-invariant
L	6.0747148243886	L(r)(E,1)/r!
Ω	0.86976383820398	Real period
R	3.492163365249	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	2548f1 40768dq1 91728er1 10192p1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192t1

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 10192t1

-4	8	-3	-7
2548f1	40768dq1	91728er1	10192p1

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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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