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Properties

Label 94050cm
Number of curves $2$
Conductor $94050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 94050cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94050.eh1 94050cm1 \([1, -1, 1, -4655, 123597]\) \(-26436959739/50578\) \(-21337593750\) \([]\) \(155520\) \(0.87148\) \(\Gamma_0(N)\)-optimal
94050.eh2 94050cm2 \([1, -1, 1, 7720, 599347]\) \(165469149/603592\) \(-185632833375000\) \([]\) \(466560\) \(1.4208\)  

Rank

sage: E.rank()
 

The elliptic curves in class 94050cm have rank \(0\).

Complex multiplication

The elliptic curves in class 94050cm do not have complex multiplication.

Modular form 94050.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 4 q^{7} + q^{8} + q^{11} + 4 q^{13} + 4 q^{14} + q^{16} - 3 q^{17} + q^{19} + O(q^{20})\) 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.