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	10192bn	Isogeny class
Conductor	10192	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	18144	Modular degree for the optimal curve
Δ	-801865465856 = -1 · 219 · 76 · 13	Discriminant
Eigenvalues	2- -3  1 7-  2 13-  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2107,56938]	[a1,a2,a3,a4,a6]
j	-2146689/1664	j-invariant
L	1.6429198876951	L(r)(E,1)/r!
Ω	0.82145994384755	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	1274n1 40768db1 91728fk1 208d1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192bn1

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
-	-3	1	-	2	-	3	6	4	2	4	3	0	5	13	12	-10	8	2	5	10	4	0	-6	-14

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Quadratic twists for elliptic curve 10192bn1

-4	8	-3	-7
1274n1	40768db1	91728fk1	208d1

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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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