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SageMath
E = EllipticCurve("gr1")
E.isogeny_class()
Elliptic curves in class 162240.gr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.gr1 | 162240es1 | \([0, 1, 0, -232925, 38431875]\) | \(621217777580032/74733890625\) | \(168130926288000000\) | \([2]\) | \(1806336\) | \(2.0360\) | \(\Gamma_0(N)\)-optimal |
| 162240.gr2 | 162240es2 | \([0, 1, 0, 335695, 197304303]\) | \(116227003261808/533935546875\) | \(-19219356000000000000\) | \([2]\) | \(3612672\) | \(2.3826\) |
Rank
sage: E.rank()
The elliptic curves in class 162240.gr have rank \(2\).
Complex multiplication
The elliptic curves in class 162240.gr do not have complex multiplication.Modular form 162240.2.a.gr
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.
