Properties

Label 102550.t
Number of curves 2
Conductor 102550
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("102550.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 102550.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.t1 102550w2 [1, -1, 1, -4779430, 4022918197] [2] 1971200  
102550.t2 102550w1 [1, -1, 1, -299430, 62598197] [2] 985600 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 102550.t have rank \(1\).

Modular form 102550.2.a.t

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.