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Properties

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

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Show commands: SageMath
E = EllipticCurve("ex1")
 
E.isogeny_class()
 

Elliptic curves in class 72450.ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.ex1 72450ey1 \([1, -1, 1, -3110, -65883]\) \(36495256013/54096\) \(4929498000\) \([2]\) \(73728\) \(0.76094\) \(\Gamma_0(N)\)-optimal
72450.ex2 72450ey2 \([1, -1, 1, -2210, -105483]\) \(-13094193293/45724644\) \(-4166658184500\) \([2]\) \(147456\) \(1.1075\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.ex

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{7} + q^{8} + 4 q^{11} - 4 q^{13} + q^{14} + q^{16} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.