Properties

Label 10830.a
Number of curves $2$
Conductor $10830$
CM no
Rank $1$
Graph

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

Elliptic curves in class 10830.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.a1 10830a2 \([1, 1, 0, -9306948, -10930905648]\) \(276288773643091/41990400\) \(13549785504819321600\) \([2]\) \(389120\) \(2.6836\)  
10830.a2 10830a1 \([1, 1, 0, -527428, -204088112]\) \(-50284268371/26542080\) \(-8564802689466040320\) \([2]\) \(194560\) \(2.3370\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10830.a have rank \(1\).

Complex multiplication

The elliptic curves in class 10830.a do not have complex multiplication.

Modular form 10830.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 2q^{7} - q^{8} + q^{9} + q^{10} - q^{12} + 2q^{13} + 2q^{14} + q^{15} + q^{16} - 2q^{17} - q^{18} + O(q^{20})\)  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.