Cremona's table of elliptic curves

1955 = 5 · 17 · 23

Field	Data	Notes
Atkin-Lehner	5- 17+ 23+	Signs for the Atkin-Lehner involutions
Class	1955b	Isogeny class
Conductor	1955	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	520	Modular degree for the optimal curve
Δ	-1221875 = -1 · 55 · 17 · 23	Discriminant
Eigenvalues	1  3 5-  4  1  0 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-34,-85]	[a1,a2,a3,a4,a6]
j	-4419017721/1221875	j-invariant
L	4.8660257370961	L(r)(E,1)/r!
Ω	0.97320514741922	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	31280be1 125120k1 17595p1 9775d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1955b1

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	3	-	4	1	0	+	-2	+	-8	10	-2	-8	1	4	-3	1	-13	8	0	-6	-1	-5	0	6

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Quadratic twists for elliptic curve 1955b1

-4	8	-3	5	-7	17	-23
31280be1	125120k1	17595p1	9775d1	95795f1	33235a1	44965b1

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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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