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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 334620bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 334620.bd2 | 334620bd1 | \([0, 0, 0, -255528, 46446777]\) | \(1213857792/89375\) | \(135858696612210000\) | \([2]\) | \(4257792\) | \(2.0335\) | \(\Gamma_0(N)\)-optimal |
| 334620.bd1 | 334620bd2 | \([0, 0, 0, -825903, -233835498]\) | \(2561648112/511225\) | \(12433787913949459200\) | \([2]\) | \(8515584\) | \(2.3801\) |
Rank
sage: E.rank()
The elliptic curves in class 334620bd have rank \(0\).
Complex multiplication
The elliptic curves in class 334620bd do not have complex multiplication.Modular form 334620.2.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 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.
