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	25872be	Isogeny class
Conductor	25872	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	1411200	Modular degree for the optimal curve
Δ	-2.6613773425916E+20	Discriminant
Eigenvalues	2- 3+  3 7+ 11-  6 -5 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3817704,-2975201424]	[a1,a2,a3,a4,a6]
Generators	[4100:224224:1]	Generators of the group modulo torsion
j	-260607143968297/11270993184	j-invariant
L	5.8103103891415	L(r)(E,1)/r!
Ω	0.053866859993816	Real period
R	1.7977380990243	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	3234h1 103488gz1 77616em1 25872db1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872be1

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	+	-	6	-5	-6	-5	-6	-4	-2	5	10	-9	2	12	-5	-5	-4	12	1	-1	6	9

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Quadratic twists for elliptic curve 25872be1

-4	8	-3	-7
3234h1	103488gz1	77616em1	25872db1

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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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