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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 162240u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.ig4 | 162240u1 | \([0, 1, 0, 620, 63350]\) | \(85184/5625\) | \(-1737651240000\) | \([2]\) | \(294912\) | \(1.0282\) | \(\Gamma_0(N)\)-optimal |
| 162240.ig3 | 162240u2 | \([0, 1, 0, -20505, 1081575]\) | \(48228544/2025\) | \(40035484569600\) | \([2, 2]\) | \(589824\) | \(1.3748\) | |
| 162240.ig1 | 162240u3 | \([0, 1, 0, -324705, 71108415]\) | \(23937672968/45\) | \(7117419479040\) | \([2]\) | \(1179648\) | \(1.7214\) | |
| 162240.ig2 | 162240u4 | \([0, 1, 0, -54305, -3440865]\) | \(111980168/32805\) | \(5188598800220160\) | \([2]\) | \(1179648\) | \(1.7214\) |
Rank
sage: E.rank()
The elliptic curves in class 162240u have rank \(0\).
Complex multiplication
The elliptic curves in class 162240u do not have complex multiplication.Modular form 162240.2.a.u
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.
