Cremona's table of elliptic curves

13632 = 2⁶ · 3 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 71-	Signs for the Atkin-Lehner involutions
Class	13632k	Isogeny class
Conductor	13632	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-848019456 = -1 · 214 · 36 · 71	Discriminant
Eigenvalues	2+ 3- -2  2  4 -2  4  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-49,1391]	[a1,a2,a3,a4,a6]
Generators	[5:36:1]	Generators of the group modulo torsion
j	-810448/51759	j-invariant
L	5.7371745084207	L(r)(E,1)/r!
Ω	1.3081308032733	Real period
R	0.73096340901904	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	13632m1 1704b1 40896n1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 13632k1

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

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Quadratic twists for elliptic curve 13632k1

-4	8	-3
13632m1	1704b1	40896n1

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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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