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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 97020.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97020.cf1 | 97020ba1 | \([0, 0, 0, -2352, -40131]\) | \(28311552/2695\) | \(136971671760\) | \([2]\) | \(129024\) | \(0.87479\) | \(\Gamma_0(N)\)-optimal |
| 97020.cf2 | 97020ba2 | \([0, 0, 0, 2793, -191394]\) | \(2963088/21175\) | \(-17219295878400\) | \([2]\) | \(258048\) | \(1.2214\) |
Rank
sage: E.rank()
The elliptic curves in class 97020.cf have rank \(1\).
Complex multiplication
The elliptic curves in class 97020.cf do not have complex multiplication.Modular form 97020.2.a.cf
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 LMFDB 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 LMFDB labels.
