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Properties

Label 162624hi
Number of curves $2$
Conductor $162624$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("hi1")
 
E.isogeny_class()
 

Elliptic curves in class 162624hi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.bf2 162624hi1 \([0, -1, 0, 191, 1729]\) \(8788/21\) \(-1831796736\) \([2]\) \(61440\) \(0.46133\) \(\Gamma_0(N)\)-optimal
162624.bf1 162624hi2 \([0, -1, 0, -1569, 20385]\) \(2450086/441\) \(76935462912\) \([2]\) \(122880\) \(0.80790\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162624hi have rank \(2\).

Complex multiplication

The elliptic curves in class 162624hi do not have complex multiplication.

Modular form 162624.2.a.hi

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{7} + q^{9} + 2 q^{13} + 2 q^{15} - 4 q^{17} - 4 q^{19} + O(q^{20})\) 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.