Cremona's table of elliptic curves

2805 = 3 · 5 · 11 · 17

Field	Data	Notes
Atkin-Lehner	3- 5+ 11- 17+	Signs for the Atkin-Lehner involutions
Class	2805d	Isogeny class
Conductor	2805	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	8736	Modular degree for the optimal curve
Δ	99845947265625 = 37 · 512 · 11 · 17	Discriminant
Eigenvalues	1 3- 5+  0 11-  2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13729,-391273]	[a1,a2,a3,a4,a6]
Generators	[-35:233:1]	Generators of the group modulo torsion
j	286150792766867209/99845947265625	j-invariant
L	4.4141196569383	L(r)(E,1)/r!
Ω	0.45366984151111	Real period
R	2.7799446413248	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	44880z1 8415n1 14025h1 30855l1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 2805d1

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	-	+	0	-	2	+	-8	0	6	-4	2	2	-12	-12	-14	-12	-2	12	-8	2	0	-4	10	14

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Quadratic twists for elliptic curve 2805d1

-4	-3	5	-11	17
44880z1	8415n1	14025h1	30855l1	47685e1

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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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