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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6480.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6480.g1 | 6480i2 | \([0, 0, 0, -3483, 127818]\) | \(-2146689/2000\) | \(-4353564672000\) | \([]\) | \(10368\) | \(1.1217\) | |
| 6480.g2 | 6480i1 | \([0, 0, 0, 357, -2998]\) | \(15166431/20480\) | \(-6794772480\) | \([]\) | \(3456\) | \(0.57238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6480.g have rank \(0\).
Complex multiplication
The elliptic curves in class 6480.g do not have complex multiplication.Modular form 6480.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
