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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 132600r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132600.f2 | 132600r1 | \([0, -1, 0, -1002708, -379626588]\) | \(27873248949250000/538367795433\) | \(2153471181732000000\) | \([2]\) | \(2654208\) | \(2.3106\) | \(\Gamma_0(N)\)-optimal |
| 132600.f1 | 132600r2 | \([0, -1, 0, -2101208, 602432412]\) | \(64122592551794500/27331783704693\) | \(437308539275088000000\) | \([2]\) | \(5308416\) | \(2.6572\) |
Rank
sage: E.rank()
The elliptic curves in class 132600r have rank \(1\).
Complex multiplication
The elliptic curves in class 132600r do not have complex multiplication.Modular form 132600.2.a.r
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.
