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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 44880.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.l1 | 44880bl2 | \([0, -1, 0, -188239776, 994128725760]\) | \(-180093466903641160790448289/4344384000\) | \(-17794596864000\) | \([]\) | \(3265920\) | \(2.9899\) | |
| 44880.l2 | 44880bl1 | \([0, -1, 0, -2322336, 1366361856]\) | \(-338173143620095981729/979226371031040\) | \(-4010911215743139840\) | \([]\) | \(1088640\) | \(2.4406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44880.l have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.l do not have complex multiplication.Modular form 44880.2.a.l
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.
