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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 168432.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 168432.j1 | 168432bj2 | \([0, -1, 0, -12605336, -17272000656]\) | \(-30526075007211889/103499257854\) | \(-751023098851697025024\) | \([]\) | \(6585600\) | \(2.8697\) | |
| 168432.j2 | 168432bj1 | \([0, -1, 0, -1976, 11678064]\) | \(-117649/8118144\) | \(-58907800792203264\) | \([]\) | \(940800\) | \(1.8968\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 168432.j have rank \(1\).
Complex multiplication
The elliptic curves in class 168432.j do not have complex multiplication.Modular form 168432.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
