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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 81200j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81200.cd2 | 81200j1 | \([0, -1, 0, -53208, -5577088]\) | \(-1041220466500/242597383\) | \(-3881558128000000\) | \([2]\) | \(442368\) | \(1.7106\) | \(\Gamma_0(N)\)-optimal |
| 81200.cd1 | 81200j2 | \([0, -1, 0, -894208, -325157088]\) | \(2471097448795250/98942809\) | \(3166169888000000\) | \([2]\) | \(884736\) | \(2.0572\) |
Rank
sage: E.rank()
The elliptic curves in class 81200j have rank \(0\).
Complex multiplication
The elliptic curves in class 81200j do not have complex multiplication.Modular form 81200.2.a.j
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.
