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	10192i	Isogeny class
Conductor	10192	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	22391824 = 24 · 72 · 134	Discriminant
Eigenvalues	2+ -1 -3 7-  1 13-  5 -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-72,-41]	[a1,a2,a3,a4,a6]
Generators	[-5:13:1]	Generators of the group modulo torsion
j	53385472/28561	j-invariant
L	2.6545697180902	L(r)(E,1)/r!
Ω	1.7409860887294	Real period
R	0.38118766934368	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	5096e1 40768cp1 91728bt1 10192a1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10192i1

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	-3	-	1	-	5	-3	-9	-6	7	7	-6	12	-7	-9	3	5	-3	-8	13	15	4	13	-14

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Quadratic twists for elliptic curve 10192i1

-4	8	-3	-7
5096e1	40768cp1	91728bt1	10192a1

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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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