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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 180336bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.t1 | 180336bj1 | \([0, -1, 0, -88367048, 309073775088]\) | \(771864882375147625/29358565696512\) | \(2902607483865462617407488\) | \([2]\) | \(22118400\) | \(3.4621\) | \(\Gamma_0(N)\)-optimal |
| 180336.t2 | 180336bj2 | \([0, -1, 0, 36665912, 1113485826544]\) | \(55138849409108375/5449537181735712\) | \(-538782022624097436320268288\) | \([2]\) | \(44236800\) | \(3.8087\) |
Rank
sage: E.rank()
The elliptic curves in class 180336bj have rank \(0\).
Complex multiplication
The elliptic curves in class 180336bj do not have complex multiplication.Modular form 180336.2.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.
