Properties

Label 89232f
Number of curves $2$
Conductor $89232$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 89232f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
89232.p2 89232f1 \([0, -1, 0, 481932, 469027584]\) \(10017976862000/82759712607\) \(-102263123366113552128\) \([2]\) \(1806336\) \(2.5209\) \(\Gamma_0(N)\)-optimal
89232.p1 89232f2 \([0, -1, 0, -6910128, 6435898416]\) \(7382814913718500/654774260283\) \(3236321579522382793728\) \([2]\) \(3612672\) \(2.8675\)  

Rank

sage: E.rank()
 

The elliptic curves in class 89232f have rank \(0\).

Complex multiplication

The elliptic curves in class 89232f do not have complex multiplication.

Modular form 89232.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + q^{11} - 4 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.