Properties

Label 127050.cr
Number of curves $4$
Conductor $127050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 127050.cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
127050.cr1 127050cv4 \([1, 0, 1, -1129901, -462377302]\) \(5763259856089/5670\) \(156949232343750\) \([2]\) \(1966080\) \(2.0173\)  
127050.cr2 127050cv2 \([1, 0, 1, -71151, -7114802]\) \(1439069689/44100\) \(1220716251562500\) \([2, 2]\) \(983040\) \(1.6707\)  
127050.cr3 127050cv1 \([1, 0, 1, -10651, 266198]\) \(4826809/1680\) \(46503476250000\) \([2]\) \(491520\) \(1.3241\) \(\Gamma_0(N)\)-optimal
127050.cr4 127050cv3 \([1, 0, 1, 19599, -23994302]\) \(30080231/9003750\) \(-249229568027343750\) \([2]\) \(1966080\) \(2.0173\)  

Rank

sage: E.rank()
 

The elliptic curves in class 127050.cr have rank \(1\).

Complex multiplication

The elliptic curves in class 127050.cr do not have complex multiplication.

Modular form 127050.2.a.cr

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + q^{12} - 2 q^{13} + q^{14} + q^{16} - 6 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.