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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 393129bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 393129.bd2 | 393129bd1 | \([0, 0, 1, -142836870, 708337790113]\) | \(-5304438784000/497763387\) | \(-30243231504247980164468643\) | \([]\) | \(62208000\) | \(3.6313\) | \(\Gamma_0(N)\)-optimal |
| 393129.bd1 | 393129bd2 | \([0, 0, 1, -11818768170, 494545705180942]\) | \(-3004935183806464000/2037123\) | \(-123772025224563489432747\) | \([]\) | \(186624000\) | \(4.1806\) |
Rank
sage: E.rank()
The elliptic curves in class 393129bd have rank \(0\).
Complex multiplication
The elliptic curves in class 393129bd do not have complex multiplication.Modular form 393129.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
