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	24336a	Isogeny class
Conductor	24336	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	22553322974208 = 210 · 33 · 138	Discriminant
Eigenvalues	2+ 3+  2  2 -4 13+  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8619,-206518]	[a1,a2,a3,a4,a6]
Generators	[-29:138:1]	Generators of the group modulo torsion
j	530604/169	j-invariant
L	6.4313474618544	L(r)(E,1)/r!
Ω	0.50795387492196	Real period
R	3.1653206026051	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	12168l2 97344dx2 24336b2 1872b2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 24336a2

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	2	-4	+	0	-2	4	0	2	10	2	-8	0	-12	-12	-6	-6	8	2	-12	4	14	10

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Quadratic twists for elliptic curve 24336a2

-4	8	-3	13
12168l2	97344dx2	24336b2	1872b2

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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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