Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72450.w1 72450a1 [1, -1, 0, -123165042, -219939523884] [2] 24772608 \(\Gamma_0(N)\)-optimal
72450.w2 72450a2 [1, -1, 0, 442082958, -1673192131884] [2] 49545216  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.w

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

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.