Properties

Label 123840.fp
Number of curves $2$
Conductor $123840$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fp1")
 
E.isogeny_class()
 

Elliptic curves in class 123840.fp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123840.fp1 123840x2 \([0, 0, 0, -3372, -74736]\) \(4792616856/46225\) \(40896921600\) \([2]\) \(98304\) \(0.85610\)  
123840.fp2 123840x1 \([0, 0, 0, -372, 864]\) \(51478848/26875\) \(2972160000\) \([2]\) \(49152\) \(0.50953\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 123840.fp have rank \(1\).

Complex multiplication

The elliptic curves in class 123840.fp do not have complex multiplication.

Modular form 123840.2.a.fp

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