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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 51894.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51894.s1 | 51894bd2 | \([1, -1, 1, -27569, 1791559]\) | \(-132651/2\) | \(-34937469906246\) | \([]\) | \(179820\) | \(1.4018\) | |
51894.s2 | 51894bd3 | \([1, -1, 1, -13154, -766623]\) | \(-1167051/512\) | \(-110419657975296\) | \([]\) | \(179820\) | \(1.4018\) | |
51894.s3 | 51894bd1 | \([1, -1, 1, 1261, 11787]\) | \(9261/8\) | \(-191700795096\) | \([]\) | \(59940\) | \(0.85248\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51894.s have rank \(0\).
Complex multiplication
The elliptic curves in class 51894.s do not have complex multiplication.Modular form 51894.2.a.s
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.