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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 54080df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54080.t1 | 54080df1 | \([0, 1, 0, -108385, -14473185]\) | \(-658489/40\) | \(-8553556565032960\) | \([]\) | \(359424\) | \(1.8120\) | \(\Gamma_0(N)\)-optimal |
| 54080.t2 | 54080df2 | \([0, 1, 0, 594655, -22769057]\) | \(108750551/64000\) | \(-13685690504052736000\) | \([]\) | \(1078272\) | \(2.3613\) |
Rank
sage: E.rank()
The elliptic curves in class 54080df have rank \(1\).
Complex multiplication
The elliptic curves in class 54080df do not have complex multiplication.Modular form 54080.2.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.
