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SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 377520.gw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.gw1 | 377520gw2 | \([0, 1, 0, -2453920, -1206421900]\) | \(169204136291/32906250\) | \(317813621583744000000\) | \([2]\) | \(10948608\) | \(2.6509\) | |
| 377520.gw2 | 377520gw1 | \([0, 1, 0, 314560, -111211212]\) | \(356400829/760500\) | \(-7345025921046528000\) | \([2]\) | \(5474304\) | \(2.3043\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.gw have rank \(0\).
Complex multiplication
The elliptic curves in class 377520.gw do not have complex multiplication.Modular form 377520.2.a.gw
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.
