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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 361920.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.u1 | 361920u1 | \([0, -1, 0, -346021, -59085659]\) | \(4474375016012824576/1110767472704565\) | \(1137425892049474560\) | \([2]\) | \(4792320\) | \(2.1749\) | \(\Gamma_0(N)\)-optimal |
| 361920.u2 | 361920u2 | \([0, -1, 0, 834959, -375824495]\) | \(3929150857812183344/5992508593577025\) | \(-98181260797165977600\) | \([2]\) | \(9584640\) | \(2.5214\) |
Rank
sage: E.rank()
The elliptic curves in class 361920.u have rank \(2\).
Complex multiplication
The elliptic curves in class 361920.u do not have complex multiplication.Modular form 361920.2.a.u
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 LMFDB 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 LMFDB labels.
