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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 92950.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92950.ce1 | 92950cg1 | \([1, 1, 1, -4313, 296031]\) | \(-117649/440\) | \(-33184311875000\) | \([]\) | \(221184\) | \(1.2801\) | \(\Gamma_0(N)\)-optimal |
92950.ce2 | 92950cg2 | \([1, 1, 1, 37937, -7055469]\) | \(80062991/332750\) | \(-25095635855468750\) | \([]\) | \(663552\) | \(1.8294\) |
Rank
sage: E.rank()
The elliptic curves in class 92950.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 92950.ce do not have complex multiplication.Modular form 92950.2.a.ce
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.