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	24336bi	Isogeny class
Conductor	24336	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	-12280707219456 = -1 · 216 · 38 · 134	Discriminant
Eigenvalues	2- 3-  1  2  2 13+ -5  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-507,-168662]	[a1,a2,a3,a4,a6]
Generators	[143:1638:1]	Generators of the group modulo torsion
j	-169/144	j-invariant
L	6.5300999131425	L(r)(E,1)/r!
Ω	0.32118756671052	Real period
R	1.6942592091441	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	3042j1 97344ex1 8112bc1 24336bn1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 24336bi1

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	2	2	+	-5	2	6	9	4	-11	-5	-10	2	1	-8	-11	-2	-14	-13	4	6	-2	-2

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Quadratic twists for elliptic curve 24336bi1

-4	8	-3	13
3042j1	97344ex1	8112bc1	24336bn1

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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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