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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6930.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6930.c1 | 6930a1 | \([1, -1, 0, -188340, -31409200]\) | \(37537160298467283/5519360000\) | \(108637562880000\) | \([2]\) | \(43008\) | \(1.7075\) | \(\Gamma_0(N)\)-optimal |
6930.c2 | 6930a2 | \([1, -1, 0, -171060, -37419184]\) | \(-28124139978713043/14526050000000\) | \(-285916242150000000\) | \([2]\) | \(86016\) | \(2.0541\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.c have rank \(0\).
Complex multiplication
The elliptic curves in class 6930.c do not have complex multiplication.Modular form 6930.2.a.c
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.