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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 193600x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 193600.bk2 | 193600x1 | \([0, 1, 0, -3195408, -2097045062]\) | \(2036792051776/107421875\) | \(190304404296875000000\) | \([2]\) | \(5529600\) | \(2.6482\) | \(\Gamma_0(N)\)-optimal |
| 193600.bk1 | 193600x2 | \([0, 1, 0, -50461033, -137985716937]\) | \(125330290485184/378125\) | \(42871776200000000000\) | \([2]\) | \(11059200\) | \(2.9948\) |
Rank
sage: E.rank()
The elliptic curves in class 193600x have rank \(1\).
Complex multiplication
The elliptic curves in class 193600x do not have complex multiplication.Modular form 193600.2.a.x
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.
