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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 13200.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13200.l1 | 13200j1 | \([0, -1, 0, -273283, 55079062]\) | \(9028656748079104/3969405\) | \(992351250000\) | \([2]\) | \(73728\) | \(1.6434\) | \(\Gamma_0(N)\)-optimal |
| 13200.l2 | 13200j2 | \([0, -1, 0, -271908, 55659312]\) | \(-555816294307024/11837848275\) | \(-47351393100000000\) | \([2]\) | \(147456\) | \(1.9899\) |
Rank
sage: E.rank()
The elliptic curves in class 13200.l have rank \(0\).
Complex multiplication
The elliptic curves in class 13200.l do not have complex multiplication.Modular form 13200.2.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.
