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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 154560cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.ch4 | 154560cs1 | \([0, -1, 0, 1855, 70497]\) | \(2691419471/9891840\) | \(-2593086504960\) | \([2]\) | \(294912\) | \(1.0649\) | \(\Gamma_0(N)\)-optimal |
| 154560.ch3 | 154560cs2 | \([0, -1, 0, -18625, 861025]\) | \(2725812332209/373262400\) | \(97848498585600\) | \([2, 2]\) | \(589824\) | \(1.4114\) | |
| 154560.ch1 | 154560cs3 | \([0, -1, 0, -287425, 59405665]\) | \(10017490085065009/235066440\) | \(61621256847360\) | \([4]\) | \(1179648\) | \(1.7580\) | |
| 154560.ch2 | 154560cs4 | \([0, -1, 0, -77505, -7417503]\) | \(196416765680689/22365315000\) | \(5862933135360000\) | \([2]\) | \(1179648\) | \(1.7580\) |
Rank
sage: E.rank()
The elliptic curves in class 154560cs have rank \(0\).
Complex multiplication
The elliptic curves in class 154560cs do not have complex multiplication.Modular form 154560.2.a.cs
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.
