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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 206310.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206310.v1 | 206310bw2 | \([1, 0, 1, -5783304, -5339717948]\) | \(144505591826923081/435185156250\) | \(64423021485072656250\) | \([2]\) | \(10813440\) | \(2.6701\) | |
206310.v2 | 206310bw1 | \([1, 0, 1, -212934, -152589404]\) | \(-7212549413161/63756517500\) | \(-9438252747656557500\) | \([2]\) | \(5406720\) | \(2.3235\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206310.v have rank \(0\).
Complex multiplication
The elliptic curves in class 206310.v do not have complex multiplication.Modular form 206310.2.a.v
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.