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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 107800.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107800.bd1 | 107800cg1 | \([0, 0, 0, -5635, 154350]\) | \(1314036/77\) | \(1159548544000\) | \([2]\) | \(98304\) | \(1.0684\) | \(\Gamma_0(N)\)-optimal |
| 107800.bd2 | 107800cg2 | \([0, 0, 0, 4165, 634550]\) | \(265302/5929\) | \(-178570475776000\) | \([2]\) | \(196608\) | \(1.4149\) |
Rank
sage: E.rank()
The elliptic curves in class 107800.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 107800.bd do not have complex multiplication.Modular form 107800.2.a.bd
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.
