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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 96600.cj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96600.cj1 | 96600ce2 | \([0, 1, 0, -768208, -259282912]\) | \(1566789944863250/925924041\) | \(29629569312000000\) | \([2]\) | \(1548288\) | \(2.1052\) | |
| 96600.cj2 | 96600ce1 | \([0, 1, 0, -39208, -5590912]\) | \(-416618810500/598934007\) | \(-9582944112000000\) | \([2]\) | \(774144\) | \(1.7586\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 96600.cj do not have complex multiplication.Modular form 96600.2.a.cj
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.
