Cremona's table of elliptic curves

6765 = 3 · 5 · 11 · 41

Field	Data	Notes
Atkin-Lehner	3+ 5+ 11+ 41+	Signs for the Atkin-Lehner involutions
Class	6765a	Isogeny class
Conductor	6765	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	2642578125 = 3 · 59 · 11 · 41	Discriminant
Eigenvalues	0 3+ 5+  2 11+  0 -5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-671,-5998]	[a1,a2,a3,a4,a6]
Generators	[-12:13:1]	Generators of the group modulo torsion
j	33460956135424/2642578125	j-invariant
L	2.6451548414231	L(r)(E,1)/r!
Ω	0.94261485136152	Real period
R	2.8061883786389	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	108240bt1 20295p1 33825p1 74415b1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6765a1

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
0	+	+	2	+	0	-5	-1	3	-2	7	-4	+	-7	8	0	10	-6	-13	9	10	3	16	6	-14

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Quadratic twists for elliptic curve 6765a1

-4	-3	5	-11
108240bt1	20295p1	33825p1	74415b1

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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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