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	25872bi	Isogeny class
Conductor	25872	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-1629936 = -1 · 24 · 33 · 73 · 11	Discriminant
Eigenvalues	2- 3+  1 7- 11+ -7  0  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-30,99]	[a1,a2,a3,a4,a6]
Generators	[5:7:1]	Generators of the group modulo torsion
j	-562432/297	j-invariant
L	4.341015601286	L(r)(E,1)/r!
Ω	2.4799589410973	Real period
R	0.87521924846167	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	6468p1 103488ij1 77616gf1 25872cm1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 25872bi1

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
-	+	1	-	+	-7	0	5	-6	9	8	-7	2	0	3	-2	-13	2	9	14	-9	0	12	-6	-12

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Quadratic twists for elliptic curve 25872bi1

-4	8	-3	-7
6468p1	103488ij1	77616gf1	25872cm1

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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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