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	3468d	Isogeny class
Conductor	3468	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	12852	Modular degree for the optimal curve
Δ	-244095704375472 = -1 · 24 · 37 · 178	Discriminant
Eigenvalues	2- 3+  2  1  0 -3 17-  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-72057,7506882]	[a1,a2,a3,a4,a6]
Generators	[193:867:1]	Generators of the group modulo torsion
j	-370720768/2187	j-invariant
L	3.4238460159825	L(r)(E,1)/r!
Ω	0.55841292831444	Real period
R	0.68126527130646	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	13872bq1 55488by1 10404o1 86700br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3468d1

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	1	0	-3	-	1	-6	-4	-9	-1	8	-1	-8	-8	0	11	-15	6	2	16	-6	-14	-3

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Quadratic twists for elliptic curve 3468d1

-4	8	-3	5	17
13872bq1	55488by1	10404o1	86700br1	3468g1

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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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