Cremona's table of elliptic curves

3408 = 2⁴ · 3 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 71-	Signs for the Atkin-Lehner involutions
Class	3408a	Isogeny class
Conductor	3408	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	468388104192 = 211 · 32 · 714	Discriminant
Eigenvalues	2+ 3+ -2  0  0 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2064,-14112]	[a1,a2,a3,a4,a6]
j	475043342114/228705129	j-invariant
L	0.74307188514555	L(r)(E,1)/r!
Ω	0.74307188514555	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1704d3 13632r4 10224a3 85200x3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3408a4

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	0	0	-6	2	-4	0	-2	8	-2	-6	4	8	2	-8	2	8	-	-6	16	-12	-6	10

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Quadratic twists for elliptic curve 3408a4

-4	8	-3	5
1704d3	13632r4	10224a3	85200x3

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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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