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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4050.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4050.g1 | 4050q2 | \([1, -1, 0, -47022, -4056364]\) | \(-1557792607653/67108864\) | \(-495338913792000\) | \([]\) | \(18720\) | \(1.5855\) | |
4050.g2 | 4050q1 | \([1, -1, 0, -447, 3761]\) | \(-1339893/4\) | \(-29524500\) | \([]\) | \(1440\) | \(0.30304\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4050.g have rank \(1\).
Complex multiplication
The elliptic curves in class 4050.g do not have complex multiplication.Modular form 4050.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.