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	6732c	Isogeny class
Conductor	6732	Conductor
∏ cp	42	Product of Tamagawa factors cp
deg	129024	Modular degree for the optimal curve
Δ	-917340374184715008 = -1 · 28 · 38 · 113 · 177	Discriminant
Eigenvalues	2- 3- -2 -5 11-  6 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20496,46094996]	[a1,a2,a3,a4,a6]
Generators	[925:28611:1]	Generators of the group modulo torsion
j	-5102271397888/4915446963867	j-invariant
L	3.0566088117249	L(r)(E,1)/r!
Ω	0.2257926591637	Real period
R	0.32231517423426	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	26928bl1 107712bn1 2244a1 74052m1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6732c1

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	-5	-	6	-	-2	-6	7	0	8	7	-4	-7	-7	-9	14	-3	0	-1	16	12	-7	12

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Quadratic twists for elliptic curve 6732c1

-4	8	-3	-11	17
26928bl1	107712bn1	2244a1	74052m1	114444c1

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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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