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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 163464r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163464.i1 | 163464r1 | \([0, -1, 0, -61168, -5802404]\) | \(210094874500/3753\) | \(452133577728\) | \([2]\) | \(387072\) | \(1.3635\) | \(\Gamma_0(N)\)-optimal |
163464.i2 | 163464r2 | \([0, -1, 0, -59208, -6193620]\) | \(-95269531250/14085009\) | \(-3393714634426368\) | \([2]\) | \(774144\) | \(1.7100\) |
Rank
sage: E.rank()
The elliptic curves in class 163464r have rank \(1\).
Complex multiplication
The elliptic curves in class 163464r do not have complex multiplication.Modular form 163464.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.