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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 127296da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 127296.cz1 | 127296da1 | \([0, 0, 0, -34284, 2443088]\) | \(23320116793/2873\) | \(549038850048\) | \([2]\) | \(294912\) | \(1.2760\) | \(\Gamma_0(N)\)-optimal |
| 127296.cz2 | 127296da2 | \([0, 0, 0, -31404, 2870480]\) | \(-17923019113/8254129\) | \(-1577388616187904\) | \([2]\) | \(589824\) | \(1.6226\) |
Rank
sage: E.rank()
The elliptic curves in class 127296da have rank \(0\).
Complex multiplication
The elliptic curves in class 127296da do not have complex multiplication.Modular form 127296.2.a.da
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.
