Properties

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

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

Elliptic curves in class 93058.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93058.a1 93058b2 \([1, 0, 1, -174996, 26364434]\) \(24553362849625/1755162752\) \(42365362032629888\) \([2]\) \(1032192\) \(1.9374\)  
93058.a2 93058b1 \([1, 0, 1, 9964, 1801746]\) \(4533086375/60669952\) \(-1464425152626688\) \([2]\) \(516096\) \(1.5908\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 93058.a have rank \(2\).

Complex multiplication

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

Modular form 93058.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - q^{7} - q^{8} + q^{9} - 4q^{11} - 2q^{12} + q^{14} + q^{16} - q^{18} - 6q^{19} + O(q^{20})\)  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 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.