Cremona's table of elliptic curves

89232 = 2⁴ · 3 · 11 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 13+	Signs for the Atkin-Lehner involutions
Class	89232cm	Isogeny class
Conductor	89232	Conductor
∏ cp	192	Product of Tamagawa factors cp
deg	1161216	Modular degree for the optimal curve
Δ	-1625615762044944384 = -1 · 216 · 33 · 114 · 137	Discriminant
Eigenvalues	2- 3-  2  0 11- 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-416472,-120408300]	[a1,a2,a3,a4,a6]
j	-404075127457/82223856	j-invariant
L	4.461562032933	L(r)(E,1)/r!
Ω	0.092949207721966	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	11154d1 6864w1	Quadratic twists by: -4 13

Hecke Eigenvalues for elliptic curve 89232cm1

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

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Quadratic twists for elliptic curve 89232cm1

-4	13
11154d1	6864w1

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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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