Cremona's table of elliptic curves

6783 = 3 · 7 · 17 · 19

Field	Data	Notes
Atkin-Lehner	3- 7+ 17- 19+	Signs for the Atkin-Lehner involutions
Class	6783d	Isogeny class
Conductor	6783	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	43200	Modular degree for the optimal curve
Δ	45875708650989 = 34 · 75 · 173 · 193	Discriminant
Eigenvalues	2 3-  1 7+ -2 -5 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-87690,-10018753]	[a1,a2,a3,a4,a6]
Generators	[-1350:353:8]	Generators of the group modulo torsion
j	74572529560399507456/45875708650989	j-invariant
L	9.0629388315562	L(r)(E,1)/r!
Ω	0.27744548447426	Real period
R	2.7221380231176	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	108528x1 20349c1 47481f1 115311i1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 6783d1

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	+	-2	-5	-	+	-6	1	6	9	-4	8	-12	-12	-3	-5	-8	0	-3	11	-12	7	-6

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Quadratic twists for elliptic curve 6783d1

-4	-3	-7	17	-19
108528x1	20349c1	47481f1	115311i1	128877e1

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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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