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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 120240.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 120240.cs1 | 120240cs2 | \([0, 0, 0, -3046107, 1964157194]\) | \(1046819248735488409/47650971093750\) | \(142285037270400000000\) | \([2]\) | \(4128768\) | \(2.6290\) | |
| 120240.cs2 | 120240cs1 | \([0, 0, 0, 103173, 116789546]\) | \(40675641638471/1996889557500\) | \(-5962680268462080000\) | \([2]\) | \(2064384\) | \(2.2824\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 120240.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 120240.cs do not have complex multiplication.Modular form 120240.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
