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SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 221760.fw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221760.fw1 | 221760dk2 | \([0, 0, 0, -52171068, -145023465008]\) | \(1314817350433665559504/190690249278375\) | \(2277592133204957184000\) | \([2]\) | \(20643840\) | \(3.1131\) | |
| 221760.fw2 | 221760dk1 | \([0, 0, 0, -2963568, -2695692008]\) | \(-3856034557002072064/1973796785296875\) | \(-1473431405036976000000\) | \([2]\) | \(10321920\) | \(2.7665\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 221760.fw have rank \(1\).
Complex multiplication
The elliptic curves in class 221760.fw do not have complex multiplication.Modular form 221760.2.a.fw
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.
