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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 145200gl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 145200.fa4 | 145200gl1 | \([0, -1, 0, -97808, 242112]\) | \(912673/528\) | \(59864589312000000\) | \([2]\) | \(1474560\) | \(1.9087\) | \(\Gamma_0(N)\)-optimal |
| 145200.fa2 | 145200gl2 | \([0, -1, 0, -1065808, -421805888]\) | \(1180932193/4356\) | \(493882861824000000\) | \([2, 2]\) | \(2949120\) | \(2.2553\) | |
| 145200.fa3 | 145200gl3 | \([0, -1, 0, -581808, -807069888]\) | \(-192100033/2371842\) | \(-268919218263168000000\) | \([2]\) | \(5898240\) | \(2.6019\) | |
| 145200.fa1 | 145200gl4 | \([0, -1, 0, -17037808, -27063101888]\) | \(4824238966273/66\) | \(7483073664000000\) | \([2]\) | \(5898240\) | \(2.6019\) |
Rank
sage: E.rank()
The elliptic curves in class 145200gl have rank \(1\).
Complex multiplication
The elliptic curves in class 145200gl do not have complex multiplication.Modular form 145200.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
