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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 213444r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
213444.k2 | 213444r1 | \([0, 0, 0, -124509, -3195731]\) | \(1792\) | \(119120893426546704\) | \([]\) | \(1701000\) | \(1.9669\) | \(\Gamma_0(N)\)-optimal |
213444.k1 | 213444r2 | \([0, 0, 0, -7595049, -8056437851]\) | \(406749952\) | \(119120893426546704\) | \([]\) | \(5103000\) | \(2.5162\) |
Rank
sage: E.rank()
The elliptic curves in class 213444r have rank \(0\).
Complex multiplication
The elliptic curves in class 213444r do not have complex multiplication.Modular form 213444.2.a.r
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.