Properties

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

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 90480bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
90480.bl1 90480bt1 \([0, 1, 0, -7976, -276300]\) \(13701674594089/31758480\) \(130082734080\) \([2]\) \(135168\) \(1.0133\) \(\Gamma_0(N)\)-optimal
90480.bl2 90480bt2 \([0, 1, 0, -5096, -475596]\) \(-3573857582569/21617820900\) \(-88546594406400\) \([2]\) \(270336\) \(1.3599\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 90480.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 2 q^{7} + q^{9} + 2 q^{11} + q^{13} - q^{15} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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 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.