Cremona's table of elliptic curves

13536 = 2⁵ · 3² · 47

Field	Data	Notes
Atkin-Lehner	2+ 3+ 47+	Signs for the Atkin-Lehner involutions
Class	13536d	Isogeny class
Conductor	13536	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	59206464 = 26 · 39 · 47	Discriminant
Eigenvalues	2+ 3+ -2 -4 -4  6  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1701,27000]	[a1,a2,a3,a4,a6]
Generators	[25:10:1]	Generators of the group modulo torsion
j	432081216/47	j-invariant
L	3.2333232182679	L(r)(E,1)/r!
Ω	1.8970793374577	Real period
R	1.7043690026169	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	13536f1 27072bl2 13536w1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 13536d1

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

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Quadratic twists for elliptic curve 13536d1

-4	8	-3
13536f1	27072bl2	13536w1

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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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