Cremona's table of elliptic curves

25872 = 2⁴ · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	25872ce	Isogeny class
Conductor	25872	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	201600	Modular degree for the optimal curve
Δ	-57755584691659008 = -1 · 28 · 35 · 78 · 115	Discriminant
Eigenvalues	2- 3- -2 7+ 11+  2  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,85636,6404712]	[a1,a2,a3,a4,a6]
Generators	[139:4584:1]	Generators of the group modulo torsion
j	47061251888/39135393	j-invariant
L	5.8461154273591	L(r)(E,1)/r!
Ω	0.22788853938451	Real period
R	5.1306796235989	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	6468b1 103488ey1 77616eq1 25872bl1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872ce1

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	3	1	7	-1	-8	-11	6	9	-1	-2	-9	4	2	-15	-6	-12	-12	0	-5

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Quadratic twists for elliptic curve 25872ce1

-4	8	-3	-7
6468b1	103488ey1	77616eq1	25872bl1

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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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