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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 244398bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
244398.bn2 | 244398bn1 | \([1, 0, 0, -2051473, -1132421851]\) | \(-6449916994998625/8532911772\) | \(-1263177179926585308\) | \([2]\) | \(5677056\) | \(2.3798\) | \(\Gamma_0(N)\)-optimal |
244398.bn1 | 244398bn2 | \([1, 0, 0, -32833983, -72418558509]\) | \(26444015547214434625/46191222\) | \(6837958612766358\) | \([2]\) | \(11354112\) | \(2.7263\) |
Rank
sage: E.rank()
The elliptic curves in class 244398bn have rank \(1\).
Complex multiplication
The elliptic curves in class 244398bn do not have complex multiplication.Modular form 244398.2.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 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.