Cremona's table of elliptic curves

36456 = 2³ · 3 · 7² · 31

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 31-	Signs for the Atkin-Lehner involutions
Class	36456i	Isogeny class
Conductor	36456	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	-8166144 = -1 · 28 · 3 · 73 · 31	Discriminant
Eigenvalues	2+ 3+  3 7- -4  3  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9,141]	[a1,a2,a3,a4,a6]
Generators	[5:14:1]	Generators of the group modulo torsion
j	-1024/93	j-invariant
L	5.9304737104071	L(r)(E,1)/r!
Ω	1.9179239045734	Real period
R	0.38651648901871	Regulator
r	1	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	72912y1 109368cc1 36456m1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 36456i1

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
+	+	3	-	-4	3	0	0	5	-9	-	-10	-9	4	4	9	0	-11	7	10	3	10	4	-14	2

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Quadratic twists for elliptic curve 36456i1

-4	-3	-7
72912y1	109368cc1	36456m1

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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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