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SageMath
E = EllipticCurve("id1")
E.isogeny_class()
Elliptic curves in class 148800id
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 148800.ke2 | 148800id1 | \([0, 1, 0, 747967, -93875937]\) | \(11298232190519/7472736000\) | \(-30608326656000000000\) | \([2]\) | \(4423680\) | \(2.4278\) | \(\Gamma_0(N)\)-optimal |
| 148800.ke1 | 148800id2 | \([0, 1, 0, -3220033, -780339937]\) | \(901456690969801/457629750000\) | \(1874451456000000000000\) | \([2]\) | \(8847360\) | \(2.7743\) |
Rank
sage: E.rank()
The elliptic curves in class 148800id have rank \(0\).
Complex multiplication
The elliptic curves in class 148800id do not have complex multiplication.Modular form 148800.2.a.id
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.
