Cremona's table of elliptic curves

3293 = 37 · 89

Field	Data	Notes
Atkin-Lehner	37+ 89+	Signs for the Atkin-Lehner involutions
Class	3293a	Isogeny class
Conductor	3293	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	368	Modular degree for the optimal curve
Δ	-121841 = -1 · 372 · 89	Discriminant
Eigenvalues	1  1  1  0  0  4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-258,1569]	[a1,a2,a3,a4,a6]
Generators	[9:-4:1]	Generators of the group modulo torsion
j	-1888690601881/121841	j-invariant
L	4.9253087061309	L(r)(E,1)/r!
Ω	3.1403853329666	Real period
R	0.78418859214932	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	52688d1 29637d1 82325c1 121841d1	Quadratic twists by: -4 -3 5 37

Hecke Eigenvalues for elliptic curve 3293a1

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	1	1	0	0	4	-3	-5	3	-2	-1	+	-8	9	0	-11	-4	6	-8	-4	-13	-10	12	+	11

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Quadratic twists for elliptic curve 3293a1

-4	-3	5	37
52688d1	29637d1	82325c1	121841d1

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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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