Properties

Label 4025.g
Number of curves 2
Conductor 4025
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4025.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4025.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4025.g1 4025b1 [1, -1, 0, -4067, -98784] [2] 3456 \(\Gamma_0(N)\)-optimal
4025.g2 4025b2 [1, -1, 0, -3442, -130659] [2] 6912  

Rank

sage: E.rank()
 

The elliptic curves in class 4025.g have rank \(0\).

Modular form 4025.2.a.g

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

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.