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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 426888.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 426888.bn1 | 426888bn1 | \([0, 0, 0, -37191, -2407174]\) | \(194672/27\) | \(789037335136512\) | \([2]\) | \(1658880\) | \(1.5850\) | \(\Gamma_0(N)\)-optimal |
| 426888.bn2 | 426888bn2 | \([0, 0, 0, 59829, -12865930]\) | \(202612/729\) | \(-85216032194743296\) | \([2]\) | \(3317760\) | \(1.9316\) |
Rank
sage: E.rank()
The elliptic curves in class 426888.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 426888.bn do not have complex multiplication.Modular form 426888.2.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.
