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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 377520.gl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.gl1 | 377520gl2 | \([0, 1, 0, -1650480, -816685740]\) | \(68523370149961/243360\) | \(1765896539996160\) | \([2]\) | \(4915200\) | \(2.1439\) | |
| 377520.gl2 | 377520gl1 | \([0, 1, 0, -101680, -13168300]\) | \(-16022066761/998400\) | \(-7244703753830400\) | \([2]\) | \(2457600\) | \(1.7974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.gl have rank \(0\).
Complex multiplication
The elliptic curves in class 377520.gl do not have complex multiplication.Modular form 377520.2.a.gl
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.
