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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 442225.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
442225.bn1 | 442225bn2 | \([0, 1, 1, -128834883, 419072256894]\) | \(7575076864/1953125\) | \(60977148688067901611328125\) | \([]\) | \(99283968\) | \(3.6570\) | \(\Gamma_0(N)\)-optimal* |
442225.bn2 | 442225bn1 | \([0, 1, 1, -44812133, -115438467231]\) | \(318767104/125\) | \(3902537516036345703125\) | \([]\) | \(33094656\) | \(3.1077\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 442225.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 442225.bn do not have complex multiplication.Modular form 442225.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.