Properties

Label 258570fh
Number of curves 2
Conductor 258570
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("258570.fh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 258570fh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
258570.fh1 258570fh1 [1, -1, 1, -20716052, -35872861449] [2] 20643840 \(\Gamma_0(N)\)-optimal
258570.fh2 258570fh2 [1, -1, 1, -3194132, -94634372361] [2] 41287680  

Rank

sage: E.rank()
 

The elliptic curves in class 258570fh have rank \(1\).

Modular form 258570.2.a.fh

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + 2q^{7} + q^{8} + q^{10} + 2q^{14} + q^{16} + q^{17} - 2q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.