Cremona's table of elliptic curves

91728 = 2⁴ · 3² · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 13-	Signs for the Atkin-Lehner involutions
Class	91728fg	Isogeny class
Conductor	91728	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	525312	Modular degree for the optimal curve
Δ	-38892103538835456 = -1 · 231 · 37 · 72 · 132	Discriminant
Eigenvalues	2- 3-  1 7- -3 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,77973,-4449382]	[a1,a2,a3,a4,a6]
Generators	[2293:110592:1]	Generators of the group modulo torsion
j	358321516679/265814016	j-invariant
L	6.584042322382	L(r)(E,1)/r!
Ω	0.20388938940283	Real period
R	2.0182641508704	Regulator
r	1	Rank of the group of rational points
S	0.99999999945146	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	11466ci1 30576ca1 91728di1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 91728fg1

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	-	-2	0	6	-9	5	-8	-4	0	0	-1	7	4	4	6	-6	13	3	-8	15

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Quadratic twists for elliptic curve 91728fg1

-4	-3	-7
11466ci1	30576ca1	91728di1

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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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