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	13632n	Isogeny class
Conductor	13632	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4096	Modular degree for the optimal curve
Δ	-23556096 = -1 · 212 · 34 · 71	Discriminant
Eigenvalues	2- 3+ -2  4  6  0  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,71,-71]	[a1,a2,a3,a4,a6]
j	9528128/5751	j-invariant
L	2.4815144978777	L(r)(E,1)/r!
Ω	1.2407572489389	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13632t1 6816c1 40896bz1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 13632n1

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	6	0	2	4	4	-6	4	-2	2	12	12	0	10	-4	-2	+	14	16	-16	6	6

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Quadratic twists for elliptic curve 13632n1

-4	8	-3
13632t1	6816c1	40896bz1

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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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