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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 29988.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29988.l1 | 29988bm2 | \([0, 0, 0, -97671, -11747554]\) | \(1609752103216/210681\) | \(13486118913792\) | \([2]\) | \(92160\) | \(1.5396\) | |
| 29988.l2 | 29988bm1 | \([0, 0, 0, -6636, -149695]\) | \(8077950976/2255067\) | \(9021963810384\) | \([2]\) | \(46080\) | \(1.1931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29988.l have rank \(1\).
Complex multiplication
The elliptic curves in class 29988.l do not have complex multiplication.Modular form 29988.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
