Cremona's table of elliptic curves

85312 = 2⁶ · 31 · 43

Field	Data	Notes
Atkin-Lehner	2- 31- 43-	Signs for the Atkin-Lehner involutions
Class	85312x	Isogeny class
Conductor	85312	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	52224	Modular degree for the optimal curve
Δ	167904935936 = 217 · 313 · 43	Discriminant
Eigenvalues	2-  0 -1 -4  1  1 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1388,-2736]	[a1,a2,a3,a4,a6]
Generators	[-36:24:1] [-16:124:1]	Generators of the group modulo torsion
j	2256223842/1281013	j-invariant
L	8.8021558696548	L(r)(E,1)/r!
Ω	0.84461508694509	Real period
R	1.7369166155735	Regulator
r	2	Rank of the group of rational points
S	0.99999999999784	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	85312b1 21328a1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 85312x1

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	-1	-4	1	1	-4	0	-6	8	-	-2	-5	-	3	1	0	12	-8	-2	-13	-10	12	-15	-9

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Quadratic twists for elliptic curve 85312x1

-4	8
85312b1	21328a1

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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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