Properties

Label 90480be
Number of curves $2$
Conductor $90480$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 90480be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90480.r1 90480be1 \([0, -1, 0, -15705, -752328]\) \(26775969499365376/3817125\) \(61074000\) \([2]\) \(82944\) \(0.90375\) \(\Gamma_0(N)\)-optimal
90480.r2 90480be2 \([0, -1, 0, -15660, -756900]\) \(-1659154206306256/19986890625\) \(-5116644000000\) \([2]\) \(165888\) \(1.2503\)  

Rank

sage: E.rank()
 

The elliptic curves in class 90480be have rank \(0\).

Complex multiplication

The elliptic curves in class 90480be do not have complex multiplication.

Modular form 90480.2.a.be

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.