Cremona's table of elliptic curves

23205 = 3 · 5 · 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	3+ 5- 7+ 13+ 17-	Signs for the Atkin-Lehner involutions
Class	23205f	Isogeny class
Conductor	23205	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	-6.7872513354206E+25	Discriminant
Eigenvalues	1 3+ 5- 7+ -4 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-13351072,396812870209]	[a1,a2,a3,a4,a6]
Generators	[283092:41548279:64]	Generators of the group modulo torsion
j	-263191692508335916938917641/67872513354206085205078125	j-invariant
L	4.6738332291409	L(r)(E,1)/r!
Ω	0.050323676425464	Real period
R	9.2875432820643	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	69615g3 116025bl3	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 23205f3

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	+	-	+	-4	+	-	4	0	-6	0	6	10	-8	-12	2	12	10	-8	-8	-6	-4	8	-6	18

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Quadratic twists for elliptic curve 23205f3

-3	5
69615g3	116025bl3

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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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