Cremona's table of elliptic curves

3468 = 2² · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 17+	Signs for the Atkin-Lehner involutions
Class	3468c	Isogeny class
Conductor	3468	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	540	Modular degree for the optimal curve
Δ	-1123632 = -1 · 24 · 35 · 172	Discriminant
Eigenvalues	2- 3+  2 -3  4  1 17+  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,23,22]	[a1,a2,a3,a4,a6]
j	278528/243	j-invariant
L	1.7886355483462	L(r)(E,1)/r!
Ω	1.7886355483462	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13872bk1 55488bn1 10404m1 86700bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3468c1

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	-3	4	1	+	7	6	-8	-5	5	-4	9	0	0	-12	1	15	-6	-10	8	10	18	-13

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Quadratic twists for elliptic curve 3468c1

-4	8	-3	5	17
13872bk1	55488bn1	10404m1	86700bm1	3468h1

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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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