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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 76230.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.ci1 | 76230cl4 | \([1, -1, 0, -406764, 99954850]\) | \(5763259856089/5670\) | \(7322623384230\) | \([2]\) | \(655360\) | \(1.7618\) | |
| 76230.ci2 | 76230cl2 | \([1, -1, 0, -25614, 1541920]\) | \(1439069689/44100\) | \(56953737432900\) | \([2, 2]\) | \(327680\) | \(1.4153\) | |
| 76230.ci3 | 76230cl1 | \([1, -1, 0, -3834, -56732]\) | \(4826809/1680\) | \(2169666187920\) | \([2]\) | \(163840\) | \(1.0687\) | \(\Gamma_0(N)\)-optimal |
| 76230.ci4 | 76230cl3 | \([1, -1, 0, 7056, 5181358]\) | \(30080231/9003750\) | \(-11628054725883750\) | \([2]\) | \(655360\) | \(1.7618\) |
Rank
sage: E.rank()
The elliptic curves in class 76230.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 76230.ci do not have complex multiplication.Modular form 76230.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
