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	3408g	Isogeny class
Conductor	3408	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-4.7813567704386E+19	Discriminant
Eigenvalues	2- 3+  3  1 -3  2 -6 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,234536,-329878544]	[a1,a2,a3,a4,a6]
Generators	[462180:60489728:27]	Generators of the group modulo torsion
j	348329658871589543/11673234302828544	j-invariant
L	3.5612430525239	L(r)(E,1)/r!
Ω	0.096909585566566	Real period
R	3.0623415902769	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	426c2 13632u2 10224p2 85200da2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3408g2

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	1	-3	2	-6	-5	6	-9	-11	-4	9	-5	-12	-6	3	-1	4	-	-7	10	6	-6	14

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Quadratic twists for elliptic curve 3408g2

-4	8	-3	5
426c2	13632u2	10224p2	85200da2

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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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