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	10192o	Isogeny class
Conductor	10192	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	15588021904 = 24 · 78 · 132	Discriminant
Eigenvalues	2- -1  1 7+  1 13- -5  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4230,107143]	[a1,a2,a3,a4,a6]
Generators	[33:49:1]	Generators of the group modulo torsion
j	90770176/169	j-invariant
L	3.8954454316439	L(r)(E,1)/r!
Ω	1.2430927971046	Real period
R	0.52227871224594	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	2548b1 40768bx1 91728dp1 10192s1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192o1

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	1	+	1	-	-5	7	1	10	-3	-11	-10	8	-9	-9	-3	11	-7	8	-3	1	4	9	2

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Quadratic twists for elliptic curve 10192o1

-4	8	-3	-7
2548b1	40768bx1	91728dp1	10192s1

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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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