Cremona's table of elliptic curves

8010 = 2 · 3² · 5 · 89

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 89+	Signs for the Atkin-Lehner involutions
Class	8010c	Isogeny class
Conductor	8010	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	121083517440000 = 212 · 312 · 54 · 89	Discriminant
Eigenvalues	2+ 3- 5+ -4  4 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-16965,-661419]	[a1,a2,a3,a4,a6]
j	740750878754641/166095360000	j-invariant
L	0.85006376633507	L(r)(E,1)/r!
Ω	0.42503188316753	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	64080t1 2670f1 40050bb1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 8010c1

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

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Quadratic twists for elliptic curve 8010c1

-4	-3	5
64080t1	2670f1	40050bb1

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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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