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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 266175bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266175.bn1 | 266175bn1 | \([1, -1, 1, -27410, -1683808]\) | \(5177717/189\) | \(83130321353625\) | \([2]\) | \(884736\) | \(1.4406\) | \(\Gamma_0(N)\)-optimal |
| 266175.bn2 | 266175bn2 | \([1, -1, 1, 10615, -6018658]\) | \(300763/35721\) | \(-15711630735835125\) | \([2]\) | \(1769472\) | \(1.7871\) |
Rank
sage: E.rank()
The elliptic curves in class 266175bn have rank \(0\).
Complex multiplication
The elliptic curves in class 266175bn do not have complex multiplication.Modular form 266175.2.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.
