Cremona's table of elliptic curves

1683 = 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	3- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	1683i	Isogeny class
Conductor	1683	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-11042163 = -1 · 310 · 11 · 17	Discriminant
Eigenvalues	2 3-  0 -3 11+ -4 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-75,-297]	[a1,a2,a3,a4,a6]
Generators	[82:23:8]	Generators of the group modulo torsion
j	-64000000/15147	j-invariant
L	4.847309013356	L(r)(E,1)/r!
Ω	0.80111725635371	Real period
R	3.0253430286963	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	26928bs1 107712cf1 561c1 42075y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1683i1

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	-	0	-3	+	-4	-	-2	-6	9	-4	2	1	6	9	-13	15	-14	-9	14	-13	0	-2	-13	14

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Quadratic twists for elliptic curve 1683i1

-4	8	-3	5	-7	-11	17
26928bs1	107712cf1	561c1	42075y1	82467s1	18513o1	28611v1

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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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