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SageMath
sage: E = EllipticCurve("6720.l1")
sage: E.isogeny_class()
Elliptic curves in class 6720bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 6720.l2 | 6720bk1 | [0, -1, 0, -336, 2646] | [2] | 3840 | \(\Gamma_0(N)\)-optimal |
| 6720.l1 | 6720bk2 | [0, -1, 0, -5481, 158025] | [2] | 7680 |
Rank
sage: E.rank()
The elliptic curves in class 6720bk have rank \(0\).
Modular form 6720.2.a.l
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.
