Properties

Label 215950.o
Number of curves 2
Conductor 215950
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("215950.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 215950.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
215950.o1 215950bb2 [1, -1, 0, -31769542, -301546607134] [] 146595456  
215950.o2 215950bb1 [1, -1, 0, -3445792, 2499871616] [] 20942208 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 215950.o have rank \(1\).

Modular form 215950.2.a.o

sage: E.q_eigenform(10)
 
\( q - q^{2} + 3q^{3} + q^{4} - 3q^{6} - q^{7} - q^{8} + 6q^{9} - 2q^{11} + 3q^{12} + 7q^{13} + q^{14} + q^{16} - 4q^{17} - 6q^{18} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.