Cremona's table of elliptic curves

6732 = 2² · 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 17-	Signs for the Atkin-Lehner involutions
Class	6732b	Isogeny class
Conductor	6732	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-314088192 = -1 · 28 · 38 · 11 · 17	Discriminant
Eigenvalues	2- 3-  2 -1 11-  2 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,96,772]	[a1,a2,a3,a4,a6]
Generators	[-4:18:1]	Generators of the group modulo torsion
j	524288/1683	j-invariant
L	4.6243708141201	L(r)(E,1)/r!
Ω	1.2154759621945	Real period
R	0.63409601916644	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26928bi1 107712bp1 2244c1 74052i1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6732b1

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	-1	-	2	-	-2	-6	3	-8	-4	-5	-8	-7	9	-1	-2	-11	4	-5	0	8	9	8

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Quadratic twists for elliptic curve 6732b1

-4	8	-3	-11	17
26928bi1	107712bp1	2244c1	74052i1	114444d1

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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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