Cremona's table of elliptic curves

105800 = 2³ · 5² · 23²

Field	Data	Notes
Atkin-Lehner	2- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	105800t	Isogeny class
Conductor	105800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	82944	Modular degree for the optimal curve
Δ	264500000000 = 28 · 59 · 232	Discriminant
Eigenvalues	2-  0 5+ -2 -3  2  6  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2300,34500]	[a1,a2,a3,a4,a6]
Generators	[-40:250:1]	Generators of the group modulo torsion
j	635904/125	j-invariant
L	5.8229420006288	L(r)(E,1)/r!
Ω	0.93045033638179	Real period
R	0.78227469228091	Regulator
r	1	Rank of the group of rational points
S	0.99999999931699	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	21160e1 105800s1	Quadratic twists by: 5 -23

Hecke Eigenvalues for elliptic curve 105800t1

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	-3	2	6	3	-	6	9	-8	-3	4	2	4	-8	7	2	1	-6	-15	-8	14	-12

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Quadratic twists for elliptic curve 105800t1

5	-23
21160e1	105800s1

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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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