Cremona's table of elliptic curves

3392 = 2⁶ · 53

Field	Data	Notes
Atkin-Lehner	2- 53-	Signs for the Atkin-Lehner involutions
Class	3392r	Isogeny class
Conductor	3392	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-46022656 = -1 · 214 · 532	Discriminant
Eigenvalues	2-  2 -2  0 -4  2  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-49,369]	[a1,a2,a3,a4,a6]
Generators	[9:24:1]	Generators of the group modulo torsion
j	-810448/2809	j-invariant
L	4.170848866642	L(r)(E,1)/r!
Ω	1.7680249438061	Real period
R	1.179522065357	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3392j2 848d1 30528bn2 84800bs2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3392r2

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	-2	0	-4	2	2	2	2	-2	-2	-10	2	-4	12	-	-12	-10	-2	-6	10	-10	-6	-10	14

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Quadratic twists for elliptic curve 3392r2

-4	8	-3	5
3392j2	848d1	30528bn2	84800bs2

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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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