Properties

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

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 124950cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.k2 124950cf1 \([1, 1, 0, 150, 1800]\) \(12061175/49572\) \(-1518142500\) \([]\) \(72576\) \(0.44436\) \(\Gamma_0(N)\)-optimal
124950.k1 124950cf2 \([1, 1, 0, -7725, 258525]\) \(-1665063952825/2829888\) \(-86665320000\) \([]\) \(217728\) \(0.99366\)  

Rank

sage: E.rank()
 

The elliptic curves in class 124950cf have rank \(2\).

Complex multiplication

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

Modular form 124950.2.a.cf

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 3 q^{11} - q^{12} - 5 q^{13} + q^{16} + q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.