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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 205350.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.v1 | 205350dq2 | \([1, 1, 0, -31145, -2129025]\) | \(-527709995441/118098\) | \(-747752249250\) | \([]\) | \(748800\) | \(1.2711\) | |
205350.v2 | 205350dq1 | \([1, 1, 0, 305, 325]\) | \(493039/288\) | \(-1823508000\) | \([]\) | \(149760\) | \(0.46642\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 205350.v have rank \(1\).
Complex multiplication
The elliptic curves in class 205350.v do not have complex multiplication.Modular form 205350.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.