Properties

Label 124950fk
Number of curves $2$
Conductor $124950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fk1")
 
E.isogeny_class()
 

Elliptic curves in class 124950fk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.ft2 124950fk1 \([1, 1, 1, 620437, 150925781]\) \(41890384817/39795300\) \(-25091935885110937500\) \([2]\) \(3096576\) \(2.4096\) \(\Gamma_0(N)\)-optimal
124950.ft1 124950fk2 \([1, 1, 1, -3238313, 1362573281]\) \(5956317014383/2172381210\) \(1369740900039444843750\) \([2]\) \(6193152\) \(2.7561\)  

Rank

sage: E.rank()
 

The elliptic curves in class 124950fk have rank \(0\).

Complex multiplication

The elliptic curves in class 124950fk do not have complex multiplication.

Modular form 124950.2.a.fk

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - q^{12} + q^{16} + q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.