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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 72828w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72828.y1 | 72828w1 | \([0, 0, 0, -877404, 316028725]\) | \(265327034368/297381\) | \(83724826600786896\) | \([2]\) | \(829440\) | \(2.1613\) | \(\Gamma_0(N)\)-optimal |
| 72828.y2 | 72828w2 | \([0, 0, 0, -656319, 479145238]\) | \(-6940769488/18000297\) | \(-81085032067962085632\) | \([2]\) | \(1658880\) | \(2.5078\) |
Rank
sage: E.rank()
The elliptic curves in class 72828w have rank \(0\).
Complex multiplication
The elliptic curves in class 72828w do not have complex multiplication.Modular form 72828.2.a.w
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.
