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SageMath
E = EllipticCurve("gl1")
E.isogeny_class()
Elliptic curves in class 340032.gl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 340032.gl1 | 340032gl2 | \([0, 1, 0, -1048321, -131104513]\) | \(486034459476995521/253095136942032\) | \(66347371578532036608\) | \([2]\) | \(10616832\) | \(2.4953\) | |
| 340032.gl2 | 340032gl1 | \([0, 1, 0, 247039, -15817473]\) | \(6360314548472639/4097346156288\) | \(-1074094710793961472\) | \([2]\) | \(5308416\) | \(2.1488\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 340032.gl have rank \(1\).
Complex multiplication
The elliptic curves in class 340032.gl do not have complex multiplication.Modular form 340032.2.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.
