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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 230640.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230640.bd1 | 230640bd2 | \([0, -1, 0, -575716200, 4960169335152]\) | \(5805223604235668521/435937500000000\) | \(1584726572793600000000000000\) | \([2]\) | \(123863040\) | \(3.9645\) | |
| 230640.bd2 | 230640bd1 | \([0, -1, 0, 34403480, 343759788400]\) | \(1238798620042199/14760960000000\) | \(-53659264348544040960000000\) | \([2]\) | \(61931520\) | \(3.6180\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 230640.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 230640.bd do not have complex multiplication.Modular form 230640.2.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.
