Cremona's table of elliptic curves

86700 = 2² · 3 · 5² · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	86700bd	Isogeny class
Conductor	86700	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	1473900000000 = 28 · 3 · 58 · 173	Discriminant
Eigenvalues	2- 3- 5+  0 -2  6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7508,-246012]	[a1,a2,a3,a4,a6]
Generators	[-48:78:1]	Generators of the group modulo torsion
j	2382032/75	j-invariant
L	8.8698210190843	L(r)(E,1)/r!
Ω	0.51386728894929	Real period
R	2.8768196264174	Regulator
r	1	Rank of the group of rational points
S	1.0000000006477	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17340e2 86700a2	Quadratic twists by: 5 17

Hecke Eigenvalues for elliptic curve 86700bd2

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	6	+	4	-4	-6	4	-2	2	-6	8	0	12	-4	-2	-2	2	-16	0	2	-14

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Quadratic twists for elliptic curve 86700bd2

5	17
17340e2	86700a2

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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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