Cremona's table of elliptic curves

3364 = 2² · 29²

Field	Data	Notes
Atkin-Lehner	2- 29+	Signs for the Atkin-Lehner involutions
Class	3364a	Isogeny class
Conductor	3364	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	-4415968335104 = -1 · 28 · 297	Discriminant
Eigenvalues	2- -1  3 -4 -3  5  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3644,133096]	[a1,a2,a3,a4,a6]
j	-35152/29	j-invariant
L	1.4222319911209	L(r)(E,1)/r!
Ω	0.71111599556043	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13456e1 53824b1 30276m1 84100c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3364a1

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
-	-1	3	-4	-3	5	6	4	-6	+	-5	-8	0	1	3	3	6	-2	8	6	16	-11	6	12	-8

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Quadratic twists for elliptic curve 3364a1

-4	8	-3	5	29
13456e1	53824b1	30276m1	84100c1	116b1

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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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