Properties

Label 259920.fp
Number of curves $2$
Conductor $259920$
CM no
Rank $1$
Graph

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

Elliptic curves in class 259920.fp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259920.fp1 259920fp1 \([0, 0, 0, -5187, -165566]\) \(-14317849/2700\) \(-2910438604800\) \([]\) \(497664\) \(1.1157\) \(\Gamma_0(N)\)-optimal
259920.fp2 259920fp2 \([0, 0, 0, 35853, 811186]\) \(4728305591/3000000\) \(-3233820672000000\) \([]\) \(1492992\) \(1.6650\)  

Rank

sage: E.rank()
 

The elliptic curves in class 259920.fp have rank \(1\).

Complex multiplication

The elliptic curves in class 259920.fp do not have complex multiplication.

Modular form 259920.2.a.fp

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} + 6 q^{11} - 5 q^{13} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.