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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 7245.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7245.j1 | 7245u1 | \([0, 0, 1, -192, -3168]\) | \(-1073741824/5325075\) | \(-3881979675\) | \([]\) | \(3456\) | \(0.52440\) | \(\Gamma_0(N)\)-optimal |
| 7245.j2 | 7245u2 | \([0, 0, 1, 1698, 77535]\) | \(742692847616/3992296875\) | \(-2910384421875\) | \([3]\) | \(10368\) | \(1.0737\) |
Rank
sage: E.rank()
The elliptic curves in class 7245.j have rank \(1\).
Complex multiplication
The elliptic curves in class 7245.j do not have complex multiplication.Modular form 7245.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
