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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 930.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
930.k1 | 930k2 | \([1, 1, 1, -661, -6817]\) | \(31942518433489/27900\) | \(27900\) | \([2]\) | \(320\) | \(0.15343\) | |
930.k2 | 930k1 | \([1, 1, 1, -41, -121]\) | \(-7633736209/230640\) | \(-230640\) | \([2]\) | \(160\) | \(-0.19315\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 930.k have rank \(0\).
Complex multiplication
The elliptic curves in class 930.k do not have complex multiplication.Modular form 930.2.a.k
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.