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	10192y	Isogeny class
Conductor	10192	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	-15195701248 = -1 · 218 · 73 · 132	Discriminant
Eigenvalues	2-  2 -2 7- -4 13+  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,96,5888]	[a1,a2,a3,a4,a6]
Generators	[2:78:1]	Generators of the group modulo torsion
j	68921/10816	j-invariant
L	5.3245443983167	L(r)(E,1)/r!
Ω	0.95915119900223	Real period
R	1.3878271756986	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1274j1 40768eb1 91728eh1 10192bk1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192y1

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
-	2	-2	-	-4	+	4	2	8	-6	4	-2	0	4	12	-2	2	-10	-4	8	4	-4	-14	-12	8

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Quadratic twists for elliptic curve 10192y1

-4	8	-3	-7
1274j1	40768eb1	91728eh1	10192bk1

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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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