Properties

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

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Show commands: SageMath
E = EllipticCurve("fs1")
 
E.isogeny_class()
 

Elliptic curves in class 124950fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.fi2 124950fs1 \([1, 1, 1, -26363, -2321719]\) \(-1102302937/616896\) \(-1134018711000000\) \([2]\) \(589824\) \(1.5920\) \(\Gamma_0(N)\)-optimal
124950.fi1 124950fs2 \([1, 1, 1, -467363, -123155719]\) \(6141556990297/1019592\) \(1874280925125000\) \([2]\) \(1179648\) \(1.9386\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 124950.2.a.fs

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - 2 q^{11} - q^{12} + 4 q^{13} + q^{16} + q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.