Properties

Label 56925.m
Number of curves 2
Conductor 56925
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("56925.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 56925.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
56925.m1 56925q2 [1, -1, 1, -278555, 56216072] [2] 368640  
56925.m2 56925q1 [1, -1, 1, -5180, 2087822] [2] 184320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 56925.m have rank \(1\).

Modular form 56925.2.a.m

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

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.