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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 120666p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 120666.p4 | 120666p1 | \([1, 1, 0, 166, 221460]\) | \(103823/4386816\) | \(-21174322950144\) | \([2]\) | \(368640\) | \(1.2359\) | \(\Gamma_0(N)\)-optimal |
| 120666.p3 | 120666p2 | \([1, 1, 0, -53914, 4710100]\) | \(3590714269297/73410624\) | \(354339060618816\) | \([2, 2]\) | \(737280\) | \(1.5825\) | |
| 120666.p2 | 120666p3 | \([1, 1, 0, -114754, -7956788]\) | \(34623662831857/14438442312\) | \(69691603297542408\) | \([2]\) | \(1474560\) | \(1.9290\) | |
| 120666.p1 | 120666p4 | \([1, 1, 0, -858354, 305731548]\) | \(14489843500598257/6246072\) | \(30148596544248\) | \([2]\) | \(1474560\) | \(1.9290\) |
Rank
sage: E.rank()
The elliptic curves in class 120666p have rank \(1\).
Complex multiplication
The elliptic curves in class 120666p do not have complex multiplication.Modular form 120666.2.a.p
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.
