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	10192bi	Isogeny class
Conductor	10192	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-146112512 = -1 · 215 · 73 · 13	Discriminant
Eigenvalues	2-  1  2 7- -1 13- -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-72,-652]	[a1,a2,a3,a4,a6]
j	-29791/104	j-invariant
L	3.0063716426472	L(r)(E,1)/r!
Ω	0.75159291066179	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1274f1 40768cs1 91728fr1 10192w1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192bi1

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	2	-	-1	-	-4	4	5	6	11	7	-3	-2	3	-2	4	-5	-1	2	-7	-1	-10	-6	-17

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Quadratic twists for elliptic curve 10192bi1

-4	8	-3	-7
1274f1	40768cs1	91728fr1	10192w1

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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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