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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 298816.by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 298816.by1 | 298816by2 | \([0, -1, 0, -23553, -23551]\) | \(5512402554625/3188422748\) | \(835825892851712\) | \([2]\) | \(1032192\) | \(1.5528\) | |
| 298816.by2 | 298816by1 | \([0, -1, 0, 5887, -5887]\) | \(86058173375/49827568\) | \(-13061997985792\) | \([2]\) | \(516096\) | \(1.2062\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 298816.by have rank \(1\).
Complex multiplication
The elliptic curves in class 298816.by do not have complex multiplication.Modular form 298816.2.a.by
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.
