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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 254144df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254144.df1 | 254144df1 | \([0, 1, 0, -39469, -3542747]\) | \(-2258403328/480491\) | \(-1446727834084544\) | \([]\) | \(1244160\) | \(1.6304\) | \(\Gamma_0(N)\)-optimal |
| 254144.df2 | 254144df2 | \([0, 1, 0, 278211, 20505629]\) | \(790939860992/517504691\) | \(-1558173703022577344\) | \([]\) | \(3732480\) | \(2.1797\) |
Rank
sage: E.rank()
The elliptic curves in class 254144df have rank \(0\).
Complex multiplication
The elliptic curves in class 254144df do not have complex multiplication.Modular form 254144.2.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.
