Properties

Label 72450eq
Number of curves $4$
Conductor $72450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eq1")
 
E.isogeny_class()
 

Elliptic curves in class 72450eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.ea4 72450eq1 \([1, -1, 1, -134780, 31100847]\) \(-23771111713777/22848457968\) \(-260258216541750000\) \([2]\) \(983040\) \(2.0379\) \(\Gamma_0(N)\)-optimal
72450.ea3 72450eq2 \([1, -1, 1, -2515280, 1535576847]\) \(154502321244119857/55101928644\) \(627645405960562500\) \([2, 2]\) \(1966080\) \(2.3844\)  
72450.ea2 72450eq3 \([1, -1, 1, -2877530, 1064651847]\) \(231331938231569617/90942310746882\) \(1035889758351202781250\) \([2]\) \(3932160\) \(2.7310\)  
72450.ea1 72450eq4 \([1, -1, 1, -40241030, 98264399847]\) \(632678989847546725777/80515134\) \(917117698218750\) \([2]\) \(3932160\) \(2.7310\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 72450.2.a.eq

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.