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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 176400df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.lj2 | 176400df1 | \([0, 0, 0, -1414875, 543226250]\) | \(46585/8\) | \(53792511091200000000\) | \([]\) | \(4354560\) | \(2.5063\) | \(\Gamma_0(N)\)-optimal |
| 176400.lj1 | 176400df2 | \([0, 0, 0, -32284875, -70550383750]\) | \(553463785/512\) | \(3442720709836800000000\) | \([]\) | \(13063680\) | \(3.0557\) |
Rank
sage: E.rank()
The elliptic curves in class 176400df have rank \(0\).
Complex multiplication
The elliptic curves in class 176400df do not have complex multiplication.Modular form 176400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
