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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 5850.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.bj1 | 5850cb2 | \([1, -1, 1, -1445, 3957]\) | \(3659383421/2056392\) | \(187388721000\) | \([2]\) | \(6144\) | \(0.85317\) | |
| 5850.bj2 | 5850cb1 | \([1, -1, 1, 355, 357]\) | \(54439939/32448\) | \(-2956824000\) | \([2]\) | \(3072\) | \(0.50660\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5850.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 5850.bj do not have complex multiplication.Modular form 5850.2.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 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.
