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SageMath
sage: E = EllipticCurve("w1")
sage: E.isogeny_class()
Elliptic curves in class 15680w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 15680.q2 | 15680w1 | [0, 1, 0, -16, -666] | [2] | 5760 | \(\Gamma_0(N)\)-optimal |
| 15680.q1 | 15680w2 | [0, 1, 0, -1241, -17081] | [2] | 11520 |
Rank
sage: E.rank()
The elliptic curves in class 15680w have rank \(0\).
Complex multiplication
The elliptic curves in class 15680w do not have complex multiplication.Modular form 15680.2.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.
