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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 9576.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.j1 | 9576i1 | \([0, 0, 0, -390, -2959]\) | \(562432000/1197\) | \(13961808\) | \([2]\) | \(2048\) | \(0.25555\) | \(\Gamma_0(N)\)-optimal |
| 9576.j2 | 9576i2 | \([0, 0, 0, -255, -5038]\) | \(-9826000/53067\) | \(-9903575808\) | \([2]\) | \(4096\) | \(0.60212\) |
Rank
sage: E.rank()
The elliptic curves in class 9576.j have rank \(1\).
Complex multiplication
The elliptic curves in class 9576.j do not have complex multiplication.Modular form 9576.2.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.
