Cremona's table of elliptic curves

2193 = 3 · 17 · 43

Field	Data	Notes
Atkin-Lehner	3- 17- 43+	Signs for the Atkin-Lehner involutions
Class	2193b	Isogeny class
Conductor	2193	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	2448	Modular degree for the optimal curve
Δ	-28023717609 = -1 · 33 · 176 · 43	Discriminant
Eigenvalues	1 3- -1 -3  3  7 17- -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1824,30883]	[a1,a2,a3,a4,a6]
Generators	[29:36:1]	Generators of the group modulo torsion
j	-670588189536889/28023717609	j-invariant
L	3.9892253338197	L(r)(E,1)/r!
Ω	1.1730524834352	Real period
R	0.18892899745427	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	35088n1 6579c1 54825b1 107457c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2193b1

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
1	-	-1	-3	3	7	-	-5	-4	-9	-4	-6	2	+	-11	-14	12	14	-12	14	2	-14	-15	-10	7

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Quadratic twists for elliptic curve 2193b1

-4	-3	5	-7	17	-43
35088n1	6579c1	54825b1	107457c1	37281a1	94299d1

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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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