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	10192be	Isogeny class
Conductor	10192	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-5089966336 = -1 · 28 · 76 · 132	Discriminant
Eigenvalues	2-  0 -2 7-  2 13- -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,49,-3430]	[a1,a2,a3,a4,a6]
j	432/169	j-invariant
L	0.6391252307878	L(r)(E,1)/r!
Ω	0.6391252307878	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2548i2 40768ck2 91728fm2 208c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192be2

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
-	0	-2	-	2	-	-6	-6	-8	2	10	-6	6	-4	-2	6	-10	2	-10	-10	-2	4	-6	6	-2

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Quadratic twists for elliptic curve 10192be2

-4	8	-3	-7
2548i2	40768ck2	91728fm2	208c1

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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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