Properties

Label 235200fc
Number of curves $2$
Conductor $235200$
CM no
Rank $0$
Graph

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

Elliptic curves in class 235200fc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.fc2 235200fc1 \([0, -1, 0, -933, -8763]\) \(16384/3\) \(16464000000\) \([2]\) \(196608\) \(0.67894\) \(\Gamma_0(N)\)-optimal
235200.fc1 235200fc2 \([0, -1, 0, -4433, 106737]\) \(109744/9\) \(790272000000\) \([2]\) \(393216\) \(1.0255\)  

Rank

sage: E.rank()
 

The elliptic curves in class 235200fc have rank \(0\).

Complex multiplication

The elliptic curves in class 235200fc do not have complex multiplication.

Modular form 235200.2.a.fc

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 2 q^{11} + 4 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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 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.