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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 56628r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56628.ba2 | 56628r1 | \([0, 0, 0, -5808, 153065]\) | \(1048576/117\) | \(2417628037968\) | \([2]\) | \(122880\) | \(1.1092\) | \(\Gamma_0(N)\)-optimal |
| 56628.ba1 | 56628r2 | \([0, 0, 0, -22143, -1104730]\) | \(3631696/507\) | \(167622210632448\) | \([2]\) | \(245760\) | \(1.4557\) |
Rank
sage: E.rank()
The elliptic curves in class 56628r have rank \(0\).
Complex multiplication
The elliptic curves in class 56628r do not have complex multiplication.Modular form 56628.2.a.r
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.
