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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 382200f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 382200.f2 | 382200f1 | \([0, -1, 0, 136792, 8132412]\) | \(1203052/819\) | \(-192709062000000000\) | \([2]\) | \(5038080\) | \(2.0053\) | \(\Gamma_0(N)\)-optimal |
| 382200.f1 | 382200f2 | \([0, -1, 0, -598208, 68402412]\) | \(50307514/24843\) | \(11691016428000000000\) | \([2]\) | \(10076160\) | \(2.3519\) |
Rank
sage: E.rank()
The elliptic curves in class 382200f have rank \(1\).
Complex multiplication
The elliptic curves in class 382200f do not have complex multiplication.Modular form 382200.2.a.f
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.
