Cremona's table of elliptic curves

1909 = 23 · 83

Field	Data	Notes
Atkin-Lehner	23- 83+	Signs for the Atkin-Lehner involutions
Class	1909a	Isogeny class
Conductor	1909	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	1909 = 23 · 83	Discriminant
Eigenvalues	0  0 -3 -2 -4 -4  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-4,2]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1] [0:1:1]	Generators of the group modulo torsion
j	7077888/1909	j-invariant
L	2.5819694832872	L(r)(E,1)/r!
Ω	4.368620266351	Real period
R	0.59102630255467	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30544o1 122176w1 17181d1 47725b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1909a1

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	0	-3	-2	-4	-4	0	-7	-	-5	-5	10	-9	-1	4	-1	3	-8	4	0	8	-7	+	-15	1

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Quadratic twists for elliptic curve 1909a1

-4	8	-3	5	-7	-23
30544o1	122176w1	17181d1	47725b1	93541a1	43907a1

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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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