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Properties

Label 83391m
Number of curves $2$
Conductor $83391$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 83391m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83391.r2 83391m1 \([0, -1, 1, -675190, -213101205]\) \(723570336280576/853577109\) \(40157287094338029\) \([]\) \(1872000\) \(2.0976\) \(\Gamma_0(N)\)-optimal
83391.r1 83391m2 \([0, -1, 1, -18945400, 31731716595]\) \(15985030403346927616/8374342621029\) \(393978326402158431549\) \([]\) \(9360000\) \(2.9024\)  

Rank

sage: E.rank()
 

The elliptic curves in class 83391m have rank \(0\).

Complex multiplication

The elliptic curves in class 83391m do not have complex multiplication.

Modular form 83391.2.a.m

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + q^{7} + q^{9} + 2 q^{10} + q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} - q^{15} - 4 q^{16} + 8 q^{17} + 2 q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.