Properties

Label 33600.fc
Number of curves $2$
Conductor $33600$
CM no
Rank $0$
Graph

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

Elliptic curves in class 33600.fc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.fc1 33600hd2 \([0, 1, 0, -22433, 1360863]\) \(-7620530425/526848\) \(-86318776320000\) \([]\) \(124416\) \(1.4250\)  
33600.fc2 33600hd1 \([0, 1, 0, 1567, 2463]\) \(2595575/1512\) \(-247726080000\) \([]\) \(41472\) \(0.87573\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33600.fc have rank \(0\).

Complex multiplication

The elliptic curves in class 33600.fc do not have complex multiplication.

Modular form 33600.2.a.fc

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + 6q^{11} + q^{13} + 3q^{17} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.