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	25872bd	Isogeny class
Conductor	25872	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	28224	Modular degree for the optimal curve
Δ	-535711427328 = -1 · 28 · 3 · 78 · 112	Discriminant
Eigenvalues	2- 3+  0 7+ 11-  3 -2  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4573,125665]	[a1,a2,a3,a4,a6]
Generators	[33:-98:1]	Generators of the group modulo torsion
j	-7168000/363	j-invariant
L	4.8523588520528	L(r)(E,1)/r!
Ω	0.91455812799853	Real period
R	0.44214055431993	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	6468k1 103488gw1 77616ef1 25872cu1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872bd1

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
-	+	0	+	-	3	-2	3	4	6	5	-5	-4	-5	6	-10	-12	-2	7	8	-9	-11	-4	-18	18

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Quadratic twists for elliptic curve 25872bd1

-4	8	-3	-7
6468k1	103488gw1	77616ef1	25872cu1

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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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