Properties

Label 46800.fc
Number of curves $2$
Conductor $46800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fc1")
 
E.isogeny_class()
 

Elliptic curves in class 46800.fc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.fc1 46800fo2 \([0, 0, 0, -507315, 138638450]\) \(38686490446661/141927552\) \(52974174928896000\) \([2]\) \(688128\) \(2.0695\)  
46800.fc2 46800fo1 \([0, 0, 0, -46515, -62350]\) \(29819839301/17252352\) \(6439405879296000\) \([2]\) \(344064\) \(1.7229\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46800.fc have rank \(1\).

Complex multiplication

The elliptic curves in class 46800.fc do not have complex multiplication.

Modular form 46800.2.a.fc

sage: E.q_eigenform(10)
 
\(q + 4 q^{7} - 6 q^{11} + q^{13} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.