Cremona's table of elliptic curves

3420 = 2² · 3² · 5 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 19-	Signs for the Atkin-Lehner involutions
Class	3420f	Isogeny class
Conductor	3420	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-315802800 = -1 · 24 · 37 · 52 · 192	Discriminant
Eigenvalues	2- 3- 5- -4 -2  6  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,168,169]	[a1,a2,a3,a4,a6]
Generators	[8:45:1]	Generators of the group modulo torsion
j	44957696/27075	j-invariant
L	3.3828443531902	L(r)(E,1)/r!
Ω	1.0541413217812	Real period
R	0.53484991105909	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13680bp1 54720ba1 1140d1 17100ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3420f1

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
-	-	-	-4	-2	6	2	-	-6	-8	-8	10	4	4	-6	-12	8	2	4	-12	-10	-8	-2	12	-14

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Quadratic twists for elliptic curve 3420f1

-4	8	-3	5	-19
13680bp1	54720ba1	1140d1	17100ba1	64980bs1

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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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