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	25872cv	Isogeny class
Conductor	25872	Conductor
∏ cp	256	Product of Tamagawa factors cp
deg	81920	Modular degree for the optimal curve
Δ	-134956823113728 = -1 · 212 · 38 · 73 · 114	Discriminant
Eigenvalues	2- 3-  0 7- 11-  4 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,10792,-351660]	[a1,a2,a3,a4,a6]
Generators	[52:594:1]	Generators of the group modulo torsion
j	98931640625/96059601	j-invariant
L	6.7875542787928	L(r)(E,1)/r!
Ω	0.31819396360372	Real period
R	0.33330467493789	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	1617d1 103488fe1 77616ew1 25872bu1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872cv1

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

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Quadratic twists for elliptic curve 25872cv1

-4	8	-3	-7
1617d1	103488fe1	77616ew1	25872bu1

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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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