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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 52272df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 52272.i3 | 52272df1 | \([0, 0, 0, 2541, -34606]\) | \(9261/8\) | \(-1567363792896\) | \([]\) | \(64800\) | \(1.0276\) | \(\Gamma_0(N)\)-optimal |
| 52272.i2 | 52272df2 | \([0, 0, 0, -26499, 2201474]\) | \(-1167051/512\) | \(-902801544708096\) | \([]\) | \(194400\) | \(1.5769\) | |
| 52272.i1 | 52272df3 | \([0, 0, 0, -55539, -5103054]\) | \(-132651/2\) | \(-285652051255296\) | \([]\) | \(194400\) | \(1.5769\) |
Rank
sage: E.rank()
The elliptic curves in class 52272df have rank \(0\).
Complex multiplication
The elliptic curves in class 52272df do not have complex multiplication.Modular form 52272.2.a.df
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.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
