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	3468f	Isogeny class
Conductor	3468	Conductor
∏ cp	132	Product of Tamagawa factors cp
deg	38016	Modular degree for the optimal curve
Δ	-18608707815918336 = -1 · 28 · 311 · 177	Discriminant
Eigenvalues	2- 3-  1 -4 -3  3 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-468565,-123784009]	[a1,a2,a3,a4,a6]
Generators	[929:15606:1]	Generators of the group modulo torsion
j	-1841198792704/3011499	j-invariant
L	3.9285089855983	L(r)(E,1)/r!
Ω	0.091229321330362	Real period
R	0.32622660428773	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	13872t1 55488f1 10404k1 86700k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3468f1

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	-4	-3	3	+	1	-3	10	-6	4	-5	-1	-2	-14	-6	-8	-12	-12	-2	14	6	16	0

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Quadratic twists for elliptic curve 3468f1

-4	8	-3	5	17
13872t1	55488f1	10404k1	86700k1	204a1

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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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