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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 6930v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6930.bj1 | 6930v1 | \([1, -1, 1, -20927, 1170279]\) | \(37537160298467283/5519360000\) | \(149022720000\) | \([2]\) | \(14336\) | \(1.1582\) | \(\Gamma_0(N)\)-optimal |
6930.bj2 | 6930v2 | \([1, -1, 1, -19007, 1392231]\) | \(-28124139978713043/14526050000000\) | \(-392203350000000\) | \([2]\) | \(28672\) | \(1.5048\) |
Rank
sage: E.rank()
The elliptic curves in class 6930v have rank \(1\).
Complex multiplication
The elliptic curves in class 6930v do not have complex multiplication.Modular form 6930.2.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 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.