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	25872cr	Isogeny class
Conductor	25872	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	622080	Modular degree for the optimal curve
Δ	-828834405727459824 = -1 · 24 · 39 · 711 · 113	Discriminant
Eigenvalues	2- 3-  3 7- 11+  7  6 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-844874,301817823]	[a1,a2,a3,a4,a6]
j	-35431687725461248/440311012911	j-invariant
L	5.0960783609507	L(r)(E,1)/r!
Ω	0.28311546449724	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6468j1 103488gt1 77616gv1 3696m1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872cr1

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	-	+	7	6	-1	0	-3	2	5	12	-8	-3	-12	-3	10	13	12	-11	-8	6	-6	-8

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Quadratic twists for elliptic curve 25872cr1

-4	8	-3	-7
6468j1	103488gt1	77616gv1	3696m1

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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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