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	25872bo	Isogeny class
Conductor	25872	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	552960	Modular degree for the optimal curve
Δ	7353610633595584512 = 232 · 33 · 78 · 11	Discriminant
Eigenvalues	2- 3+ -2 7- 11+ -2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-505304,-45569040]	[a1,a2,a3,a4,a6]
Generators	[-9116:310219:64]	Generators of the group modulo torsion
j	29609739866953/15259926528	j-invariant
L	2.800180245002	L(r)(E,1)/r!
Ω	0.18933374848694	Real period
R	7.3948259815794	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3234o1 103488io1 77616gk1 3696z1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872bo1

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	-8	-4	2	8	6	-6	-8	4	10	4	14	4	4	14	8	4	14	-18

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Quadratic twists for elliptic curve 25872bo1

-4	8	-3	-7
3234o1	103488io1	77616gk1	3696z1

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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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