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SageMath
E = EllipticCurve("gj1")
E.isogeny_class()
Elliptic curves in class 121968gj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121968.q1 | 121968gj1 | \([0, 0, 0, -759, -8206]\) | \(-2141392/49\) | \(-1106493696\) | \([]\) | \(69120\) | \(0.52300\) | \(\Gamma_0(N)\)-optimal |
| 121968.q2 | 121968gj2 | \([0, 0, 0, 3201, -35926]\) | \(160630448/117649\) | \(-2656691364096\) | \([]\) | \(207360\) | \(1.0723\) |
Rank
sage: E.rank()
The elliptic curves in class 121968gj have rank \(1\).
Complex multiplication
The elliptic curves in class 121968gj do not have complex multiplication.Modular form 121968.2.a.gj
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 Cremona 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 Cremona labels.
