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	10192g	Isogeny class
Conductor	10192	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-21926008832 = -1 · 211 · 77 · 13	Discriminant
Eigenvalues	2+ -1  0 7- -3 13- -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-408,-7664]	[a1,a2,a3,a4,a6]
Generators	[40:196:1]	Generators of the group modulo torsion
j	-31250/91	j-invariant
L	3.2787656510654	L(r)(E,1)/r!
Ω	0.49149066901272	Real period
R	0.83388298542159	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	5096c1 40768co1 91728bi1 1456a1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192g1

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	0	-	-3	-	-4	2	-1	4	9	3	5	-4	9	-4	10	-5	-11	16	-11	5	-4	2	7

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Quadratic twists for elliptic curve 10192g1

-4	8	-3	-7
5096c1	40768co1	91728bi1	1456a1

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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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