Properties

Label 58870.d
Number of curves $4$
Conductor $58870$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58870.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58870.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58870.d1 58870a4 [1, -1, 0, -225125, -41055189] [2] 387072  
58870.d2 58870a3 [1, -1, 0, -73745, 7221575] [2] 387072  
58870.d3 58870a2 [1, -1, 0, -14875, -561039] [2, 2] 193536  
58870.d4 58870a1 [1, -1, 0, 1945, -53075] [2] 96768 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 58870.d have rank \(1\).

Modular form 58870.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} - 3q^{9} + q^{10} - 4q^{11} - 6q^{13} + q^{14} + q^{16} - 2q^{17} + 3q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.