Cremona's table of elliptic curves

81312 = 2⁵ · 3 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	81312bk	Isogeny class
Conductor	81312	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	99840	Modular degree for the optimal curve
Δ	24989454336 = 212 · 3 · 75 · 112	Discriminant
Eigenvalues	2- 3- -1 7+ 11-  4  5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-19741,1061003]	[a1,a2,a3,a4,a6]
j	1716753094144/50421	j-invariant
L	2.223501037975	L(r)(E,1)/r!
Ω	1.1117505207504	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	81312j1 81312v1	Quadratic twists by: -4 -11

Hecke Eigenvalues for elliptic curve 81312bk1

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	+	-	4	5	-2	-4	2	4	-6	-2	-7	-1	-2	-9	10	-7	6	-8	0	7	-7	-4

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Quadratic twists for elliptic curve 81312bk1

-4	-11
81312j1	81312v1

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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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