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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 219024.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 219024.cs1 | 219024br1 | \([0, 0, 0, -16731, -909558]\) | \(-35937/4\) | \(-57651097780224\) | \([]\) | \(673920\) | \(1.3778\) | \(\Gamma_0(N)\)-optimal |
| 219024.cs2 | 219024br2 | \([0, 0, 0, 104949, 1305018]\) | \(109503/64\) | \(-74715822723170304\) | \([]\) | \(2021760\) | \(1.9271\) |
Rank
sage: E.rank()
The elliptic curves in class 219024.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 219024.cs do not have complex multiplication.Modular form 219024.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
