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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2760.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2760.g1 | 2760g2 | \([0, -1, 0, -960, -9108]\) | \(47825527682/8926875\) | \(18282240000\) | \([2]\) | \(2304\) | \(0.68713\) | |
2760.g2 | 2760g1 | \([0, -1, 0, 120, -900]\) | \(185073116/419175\) | \(-429235200\) | \([2]\) | \(1152\) | \(0.34056\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2760.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2760.g do not have complex multiplication.Modular form 2760.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.