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	24336i	Isogeny class
Conductor	24336	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	291858682512384 = 210 · 310 · 136	Discriminant
Eigenvalues	2+ 3- -2  0 -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-37011,-2614430]	[a1,a2,a3,a4,a6]
Generators	[-117:338:1] [233:1188:1]	Generators of the group modulo torsion
j	1556068/81	j-invariant
L	7.0371267438164	L(r)(E,1)/r!
Ω	0.3453188692859	Real period
R	5.0946584227856	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12168q4 97344fb3 8112k4 144b3	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 24336i3

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

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Quadratic twists for elliptic curve 24336i3

-4	8	-3	13
12168q4	97344fb3	8112k4	144b3

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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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