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Properties

Label 114240.fc
Number of curves $2$
Conductor $114240$
CM no
Rank $0$
Graph

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

Elliptic curves in class 114240.fc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114240.fc1 114240hg2 \([0, -1, 0, -2411745, 1440612225]\) \(5918043195362419129/8515734343200\) \(2232348663663820800\) \([2]\) \(2949120\) \(2.4232\)  
114240.fc2 114240hg1 \([0, -1, 0, -107745, 35633025]\) \(-527690404915129/1782829440000\) \(-467358040719360000\) \([2]\) \(1474560\) \(2.0767\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 114240.fc have rank \(0\).

Complex multiplication

The elliptic curves in class 114240.fc do not have complex multiplication.

Modular form 114240.2.a.fc

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} + 2 q^{11} - 4 q^{13} - q^{15} - q^{17} - 6 q^{19} + O(q^{20})\) 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.