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	10192k	Isogeny class
Conductor	10192	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-134296804096 = -1 · 28 · 79 · 13	Discriminant
Eigenvalues	2+ -2  1 7- -4 13-  6  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-65,17611]	[a1,a2,a3,a4,a6]
Generators	[-26:49:1]	Generators of the group modulo torsion
j	-1024/4459	j-invariant
L	3.1185977295725	L(r)(E,1)/r!
Ω	0.83268763057148	Real period
R	1.8726096167852	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	5096k1 40768cv1 91728bl1 1456b1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192k1

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	1	-	-4	-	6	1	-1	3	-7	-10	10	7	-9	3	0	-6	6	-10	11	3	11	7	-17

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Quadratic twists for elliptic curve 10192k1

-4	8	-3	-7
5096k1	40768cv1	91728bl1	1456b1

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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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