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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 50820w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50820.v1 | 50820w1 | \([0, 1, 0, -645, -2532]\) | \(1048576/525\) | \(14881112400\) | \([2]\) | \(33600\) | \(0.64473\) | \(\Gamma_0(N)\)-optimal |
50820.v2 | 50820w2 | \([0, 1, 0, 2380, -17052]\) | \(3286064/2205\) | \(-1000010753280\) | \([2]\) | \(67200\) | \(0.99131\) |
Rank
sage: E.rank()
The elliptic curves in class 50820w have rank \(0\).
Complex multiplication
The elliptic curves in class 50820w do not have complex multiplication.Modular form 50820.2.a.w
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 Cremona 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 Cremona labels.