Properties

Label 72450.ek
Number of curves $2$
Conductor $72450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ek1")
 
E.isogeny_class()
 

Elliptic curves in class 72450.ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.ek1 72450el1 \([1, -1, 1, -1162130, 482148497]\) \(15238420194810961/12619514880\) \(143744161680000000\) \([2]\) \(1290240\) \(2.2206\) \(\Gamma_0(N)\)-optimal
72450.ek2 72450el2 \([1, -1, 1, -910130, 696852497]\) \(-7319577278195281/14169067365600\) \(-161394532961287500000\) \([2]\) \(2580480\) \(2.5672\)  

Rank

sage: E.rank()
 

The elliptic curves in class 72450.ek have rank \(1\).

Complex multiplication

The elliptic curves in class 72450.ek do not have complex multiplication.

Modular form 72450.2.a.ek

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} - 2 q^{13} + q^{14} + q^{16} - 4 q^{17} + 8 q^{19} + O(q^{20})\) 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 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.