Cremona's table of elliptic curves

3249 = 3² · 19²

Field	Data	Notes
Atkin-Lehner	3- 19-	Signs for the Atkin-Lehner involutions
Class	3249f	Isogeny class
Conductor	3249	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	-38478247358517819 = -1 · 316 · 197	Discriminant
Eigenvalues	-2 3- -1  3  3  6 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,63897,-7100780]	[a1,a2,a3,a4,a6]
Generators	[247:4873:1]	Generators of the group modulo torsion
j	841232384/1121931	j-invariant
L	1.9762864062807	L(r)(E,1)/r!
Ω	0.19421273296953	Real period
R	1.2719856057216	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	51984cq1 1083c1 81225bi1 171c1	Quadratic twists by: -4 -3 5 -19

Hecke Eigenvalues for elliptic curve 3249f1

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	-	-1	3	3	6	-3	-	-4	-10	-2	-8	-8	-1	-3	-6	0	7	-8	12	-11	0	-4	10	2

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Quadratic twists for elliptic curve 3249f1

-4	-3	5	-19
51984cq1	1083c1	81225bi1	171c1

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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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