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SageMath
E = EllipticCurve("ch1")
E.isogeny_class()
Elliptic curves in class 107712ch
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 107712.ei3 | 107712ch1 | \([0, 0, 0, -4769004, 3606865072]\) | \(62768149033310713/6915442583808\) | \(1321561658122838212608\) | \([2]\) | \(5898240\) | \(2.7861\) | \(\Gamma_0(N)\)-optimal |
| 107712.ei2 | 107712ch2 | \([0, 0, 0, -18086124, -25738740560]\) | \(3423676911662954233/483711578981136\) | \(92438722268954137460736\) | \([2, 2]\) | \(11796480\) | \(3.1327\) | |
| 107712.ei4 | 107712ch3 | \([0, 0, 0, 29502996, -138334598480]\) | \(14861225463775641287/51859390496937804\) | \(-9910483857510933231304704\) | \([2]\) | \(23592960\) | \(3.4793\) | |
| 107712.ei1 | 107712ch4 | \([0, 0, 0, -278749164, -1791261643088]\) | \(12534210458299016895673/315581882565708\) | \(60308636929989314347008\) | \([2]\) | \(23592960\) | \(3.4793\) |
Rank
sage: E.rank()
The elliptic curves in class 107712ch have rank \(0\).
Complex multiplication
The elliptic curves in class 107712ch do not have complex multiplication.Modular form 107712.2.a.ch
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
