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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 7920.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7920.u1 | 7920p3 | \([0, 0, 0, -14547, -641486]\) | \(228027144098/12890625\) | \(19245600000000\) | \([2]\) | \(24576\) | \(1.3037\) | |
| 7920.u2 | 7920p2 | \([0, 0, 0, -2667, 40426]\) | \(2810381476/680625\) | \(508083840000\) | \([2, 2]\) | \(12288\) | \(0.95708\) | |
| 7920.u3 | 7920p1 | \([0, 0, 0, -2487, 47734]\) | \(9115564624/825\) | \(153964800\) | \([2]\) | \(6144\) | \(0.61051\) | \(\Gamma_0(N)\)-optimal |
| 7920.u4 | 7920p4 | \([0, 0, 0, 6333, 254626]\) | \(18814587262/29648025\) | \(-44264264140800\) | \([2]\) | \(24576\) | \(1.3037\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.u have rank \(1\).
Complex multiplication
The elliptic curves in class 7920.u do not have complex multiplication.Modular form 7920.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
