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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 19110.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19110.j1 | 19110e2 | \([1, 1, 0, -18267, -239931]\) | \(1965479081566447/1069453125000\) | \(366822421875000\) | \([2]\) | \(92160\) | \(1.4855\) | |
| 19110.j2 | 19110e1 | \([1, 1, 0, 4413, -26739]\) | \(27699861384593/17058600000\) | \(-5851099800000\) | \([2]\) | \(46080\) | \(1.1390\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19110.j have rank \(1\).
Complex multiplication
The elliptic curves in class 19110.j do not have complex multiplication.Modular form 19110.2.a.j
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.
