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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 198744de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 198744.dz1 | 198744de1 | \([0, 1, 0, -5393691, -4531457358]\) | \(1909913257984/129730653\) | \(1178720782174408204368\) | \([2]\) | \(15482880\) | \(2.7918\) | \(\Gamma_0(N)\)-optimal |
| 198744.dz2 | 198744de2 | \([0, 1, 0, 4667724, -19482720048]\) | \(77366117936/1172914587\) | \(-170511905082283116049152\) | \([2]\) | \(30965760\) | \(3.1384\) |
Rank
sage: E.rank()
The elliptic curves in class 198744de have rank \(1\).
Complex multiplication
The elliptic curves in class 198744de do not have complex multiplication.Modular form 198744.2.a.de
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
