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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 127296i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 127296.q1 | 127296i1 | \([0, 0, 0, -20856, -737656]\) | \(1343969093632/462866157\) | \(345527734735872\) | \([2]\) | \(294912\) | \(1.4915\) | \(\Gamma_0(N)\)-optimal |
| 127296.q2 | 127296i2 | \([0, 0, 0, 61764, -5133040]\) | \(2181636984368/2215505331\) | \(-26461853881122816\) | \([2]\) | \(589824\) | \(1.8381\) |
Rank
sage: E.rank()
The elliptic curves in class 127296i have rank \(2\).
Complex multiplication
The elliptic curves in class 127296i do not have complex multiplication.Modular form 127296.2.a.i
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.
