Cremona's table of elliptic curves

24336 = 2⁴ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	24336bp	Isogeny class
Conductor	24336	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16128	Modular degree for the optimal curve
Δ	-68976790272 = -1 · 28 · 313 · 132	Discriminant
Eigenvalues	2- 3-  2  1 -2 13+  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-624,-13988]	[a1,a2,a3,a4,a6]
Generators	[66:482:1]	Generators of the group modulo torsion
j	-851968/2187	j-invariant
L	6.6351211896179	L(r)(E,1)/r!
Ω	0.44438983638781	Real period
R	3.7327143007764	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	6084g1 97344fi1 8112bf1 24336bu1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 24336bp1

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	1	-2	+	4	4	6	-6	-1	-10	-4	-1	10	-8	2	-5	-7	-10	7	-17	-12	-16	-13

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Quadratic twists for elliptic curve 24336bp1

-4	8	-3	13
6084g1	97344fi1	8112bf1	24336bu1

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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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