Cremona's table of elliptic curves

24864 = 2⁵ · 3 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 37-	Signs for the Atkin-Lehner involutions
Class	24864p	Isogeny class
Conductor	24864	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	16384	Modular degree for the optimal curve
Δ	28167580224 = 26 · 38 · 72 · 372	Discriminant
Eigenvalues	2- 3+ -2 7+  0 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2014,-33176]	[a1,a2,a3,a4,a6]
Generators	[700:18468:1]	Generators of the group modulo torsion
j	14123351136448/440118441	j-invariant
L	2.8866841676007	L(r)(E,1)/r!
Ω	0.71399513260233	Real period
R	4.0430025861373	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	24864ba1 49728ea2 74592i1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 24864p1

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	+	0	-2	-2	-4	-4	-2	0	-	2	4	8	-2	4	14	0	0	10	4	12	-18	-10

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Quadratic twists for elliptic curve 24864p1

-4	8	-3
24864ba1	49728ea2	74592i1

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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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