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Properties

Label 23465a
Number of curves $2$
Conductor $23465$
CM no
Rank $1$
Graph

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

Elliptic curves in class 23465a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23465.d1 23465a1 \([1, 1, 0, -368, -733]\) \(117649/65\) \(3057982265\) \([2]\) \(13104\) \(0.51060\) \(\Gamma_0(N)\)-optimal
23465.d2 23465a2 \([1, 1, 0, 1437, -3982]\) \(6967871/4225\) \(-198768847225\) \([2]\) \(26208\) \(0.85718\)  

Rank

sage: E.rank()
 

The elliptic curves in class 23465a have rank \(1\).

Complex multiplication

The elliptic curves in class 23465a do not have complex multiplication.

Modular form 23465.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} - q^{4} - q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} + q^{9} - q^{10} + 2 q^{11} - 2 q^{12} + q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + O(q^{20})\) 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.