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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 92778.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92778.g1 | 92778i2 | \([1, 0, 1, -285736, 58768382]\) | \(-1167940433374113625/78447412008\) | \(-173290333125672\) | \([]\) | \(933120\) | \(1.7874\) | |
92778.g2 | 92778i1 | \([1, 0, 1, -211, 224336]\) | \(-467103625/9843350202\) | \(-21743960596218\) | \([]\) | \(311040\) | \(1.2381\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92778.g have rank \(2\).
Complex multiplication
The elliptic curves in class 92778.g do not have complex multiplication.Modular form 92778.2.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.