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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 388416r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.r2 | 388416r1 | \([0, -1, 0, -268577, 226425249]\) | \(-68921/672\) | \(-20890531399200669696\) | \([]\) | \(10444800\) | \(2.3895\) | \(\Gamma_0(N)\)-optimal |
| 388416.r1 | 388416r2 | \([0, -1, 0, -15990177, -34541578719]\) | \(-14544652121/8168202\) | \(-253925714815496590196736\) | \([]\) | \(52224000\) | \(3.1942\) |
Rank
sage: E.rank()
The elliptic curves in class 388416r have rank \(0\).
Complex multiplication
The elliptic curves in class 388416r do not have complex multiplication.Modular form 388416.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
