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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 97344cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.bi2 | 97344cf1 | \([0, 0, 0, -949611, 575042780]\) | \(-420526439488/390971529\) | \(-88046632217432356416\) | \([2]\) | \(2064384\) | \(2.5236\) | \(\Gamma_0(N)\)-optimal |
| 97344.bi1 | 97344cf2 | \([0, 0, 0, -17657796, 28551227744]\) | \(42246001231552/14414517\) | \(207753182255425277952\) | \([2]\) | \(4128768\) | \(2.8702\) |
Rank
sage: E.rank()
The elliptic curves in class 97344cf have rank \(0\).
Complex multiplication
The elliptic curves in class 97344cf do not have complex multiplication.Modular form 97344.2.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 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.
