Cremona's table of elliptic curves

86730 = 2 · 3 · 5 · 7² · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 7- 59-	Signs for the Atkin-Lehner involutions
Class	86730bp	Isogeny class
Conductor	86730	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	589824	Modular degree for the optimal curve
Δ	637585343514000 = 24 · 38 · 53 · 77 · 59	Discriminant
Eigenvalues	2+ 3- 5- 7- -4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-57993,-5241092]	[a1,a2,a3,a4,a6]
Generators	[-136:435:1]	Generators of the group modulo torsion
j	183337554283129/5419386000	j-invariant
L	5.1000995530889	L(r)(E,1)/r!
Ω	0.30820639391259	Real period
R	0.34474325059273	Regulator
r	1	Rank of the group of rational points
S	0.99999999935809	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12390c1	Quadratic twists by: -7

Hecke Eigenvalues for elliptic curve 86730bp1

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
+	-	-	-	-4	-2	-6	-4	0	6	-8	10	-2	4	-8	-6	-	-6	12	0	14	0	16	6	14

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Quadratic twists for elliptic curve 86730bp1

-7
12390c1

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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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