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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 54720.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54720.bn1 | 54720s2 | \([0, 0, 0, -13435788, 18955830512]\) | \(1403607530712116449/39475350\) | \(7543856863641600\) | \([2]\) | \(1720320\) | \(2.5571\) | |
54720.bn2 | 54720s1 | \([0, 0, 0, -838668, 296976368]\) | \(-341370886042369/1817528220\) | \(-347335051805982720\) | \([2]\) | \(860160\) | \(2.2105\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54720.bn have rank \(2\).
Complex multiplication
The elliptic curves in class 54720.bn do not have complex multiplication.Modular form 54720.2.a.bn
sage: E.q_eigenform(10)
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.