Cremona's table of elliptic curves

3364 = 2² · 29²

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	3364c	Isogeny class
Conductor	3364	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	100800	Modular degree for the optimal curve
Δ	-4415968335104 = -1 · 28 · 297	Discriminant
Eigenvalues	2-  3  3  4  1 -3 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4062871,-3152083138]	[a1,a2,a3,a4,a6]
j	-48707390098512/29	j-invariant
L	5.2105956955412	L(r)(E,1)/r!
Ω	0.053169343832053	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	49	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13456k1 53824k1 30276l1 84100f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3364c1

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	3	4	1	-3	-2	-4	-6	+	-9	8	8	5	7	-5	-10	-10	8	-2	0	1	6	-12	0

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Quadratic twists for elliptic curve 3364c1

-4	8	-3	5	29
13456k1	53824k1	30276l1	84100f1	116a1

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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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