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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 36300bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36300.br2 | 36300bj1 | \([0, 1, 0, -4033, -1597312]\) | \(-16384/2475\) | \(-1096153368750000\) | \([2]\) | \(138240\) | \(1.5653\) | \(\Gamma_0(N)\)-optimal |
| 36300.br1 | 36300bj2 | \([0, 1, 0, -230908, -42434812]\) | \(192143824/1815\) | \(12861532860000000\) | \([2]\) | \(276480\) | \(1.9118\) |
Rank
sage: E.rank()
The elliptic curves in class 36300bj have rank \(0\).
Complex multiplication
The elliptic curves in class 36300bj do not have complex multiplication.Modular form 36300.2.a.bj
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.
