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Properties

Label 93058a
Number of curves $2$
Conductor $93058$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 93058a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93058.e2 93058a1 \([1, -1, 0, -2366, 206784]\) \(-60698457/725788\) \(-17518757929372\) \([2]\) \(199680\) \(1.2230\) \(\Gamma_0(N)\)-optimal
93058.e1 93058a2 \([1, -1, 0, -68836, 6946842]\) \(1494447319737/5411854\) \(130628999342926\) \([2]\) \(399360\) \(1.5696\)  

Rank

sage: E.rank()
 

The elliptic curves in class 93058a have rank \(1\).

Complex multiplication

The elliptic curves in class 93058a do not have complex multiplication.

Modular form 93058.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 2 q^{5} - q^{7} - q^{8} - 3 q^{9} - 2 q^{10} + 4 q^{11} + 4 q^{13} + q^{14} + q^{16} + 3 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.