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	10192y	Isogeny class
Conductor	10192	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	321009188864 = 215 · 73 · 134	Discriminant
Eigenvalues	2-  2 -2 7- -4 13+  4  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4384,109824]	[a1,a2,a3,a4,a6]
Generators	[-30:462:1]	Generators of the group modulo torsion
j	6634074439/228488	j-invariant
L	5.3245443983167	L(r)(E,1)/r!
Ω	0.95915119900223	Real period
R	2.7756543513972	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1274j2 40768eb2 91728eh2 10192bk2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192y2

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	-2	-	-4	+	4	2	8	-6	4	-2	0	4	12	-2	2	-10	-4	8	4	-4	-14	-12	8

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Quadratic twists for elliptic curve 10192y2

-4	8	-3	-7
1274j2	40768eb2	91728eh2	10192bk2

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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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