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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 468468.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 468468.bn1 | 468468bn1 | \([0, 0, 0, -11661, 503113]\) | \(-84098304/3773\) | \(-7867389754224\) | \([]\) | \(1181952\) | \(1.2390\) | \(\Gamma_0(N)\)-optimal |
| 468468.bn2 | 468468bn2 | \([0, 0, 0, 59319, 1364337]\) | \(15185664/9317\) | \(-14162746588374384\) | \([]\) | \(3545856\) | \(1.7883\) |
Rank
sage: E.rank()
The elliptic curves in class 468468.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 468468.bn do not have complex multiplication.Modular form 468468.2.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.
