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	25872d	Isogeny class
Conductor	25872	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	131194635264 = 210 · 32 · 76 · 112	Discriminant
Eigenvalues	2+ 3+ -2 7- 11+ -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1584,17424]	[a1,a2,a3,a4,a6]
Generators	[-42:90:1] [-16:196:1]	Generators of the group modulo torsion
j	3650692/1089	j-invariant
L	6.2208023087463	L(r)(E,1)/r!
Ω	0.96531687335018	Real period
R	1.6110777922995	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12936j2 103488in2 77616ch2 528d2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872d2

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	-6	0	-4	2	0	-10	-6	8	-4	-6	-12	-2	-4	-12	14	-16	-12	-10	14

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Quadratic twists for elliptic curve 25872d2

-4	8	-3	-7
12936j2	103488in2	77616ch2	528d2

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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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