Cremona's table of elliptic curves

3416 = 2³ · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 7- 61-	Signs for the Atkin-Lehner involutions
Class	3416b	Isogeny class
Conductor	3416	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	437248 = 210 · 7 · 61	Discriminant
Eigenvalues	2+ -3  2 7-  1  4 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19,-2]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	740772/427	j-invariant
L	2.5745671647434	L(r)(E,1)/r!
Ω	2.491663728351	Real period
R	0.51663616070038	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	6832b1 27328i1 30744i1 85400w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3416b1

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
+	-3	2	-	1	4	-3	-7	-3	-2	-2	-2	0	-1	1	0	-8	-	-5	5	0	9	-11	-3	-6

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Quadratic twists for elliptic curve 3416b1

-4	8	-3	5	-7
6832b1	27328i1	30744i1	85400w1	23912a1

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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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