Cremona's table of elliptic curves

45864 = 2³ · 3² · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 13-	Signs for the Atkin-Lehner involutions
Class	45864by	Isogeny class
Conductor	45864	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	200704	Modular degree for the optimal curve
Δ	-881121331673856 = -1 · 28 · 38 · 79 · 13	Discriminant
Eigenvalues	2- 3- -3 7-  2 13- -2  7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-78204,8537956]	[a1,a2,a3,a4,a6]
Generators	[392:6174:1]	Generators of the group modulo torsion
j	-7023616/117	j-invariant
L	4.8965047672612	L(r)(E,1)/r!
Ω	0.49999148912902	Real period
R	1.2241470289276	Regulator
r	1	Rank of the group of rational points
S	1.0000000000021	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	91728bw1 15288p1 45864bl1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 45864by1

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	-	2	-	-2	7	1	3	-1	-8	2	-7	1	3	-12	10	12	-4	3	1	-11	-9	7

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Quadratic twists for elliptic curve 45864by1

-4	-3	-7
91728bw1	15288p1	45864bl1

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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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