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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 83790.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83790.j1 | 83790d2 | \([1, -1, 0, -19560, -580000]\) | \(260549802603/104256800\) | \(331174123106400\) | \([2]\) | \(460800\) | \(1.4843\) | |
| 83790.j2 | 83790d1 | \([1, -1, 0, 3960, -67264]\) | \(2161700757/1848320\) | \(-5871230991360\) | \([2]\) | \(230400\) | \(1.1377\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 83790.j have rank \(0\).
Complex multiplication
The elliptic curves in class 83790.j do not have complex multiplication.Modular form 83790.2.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.
