Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 5328u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5328.k3 | 5328u1 | \([0, 0, 0, -480, 4016]\) | \(4096000/37\) | \(110481408\) | \([]\) | \(1440\) | \(0.36592\) | \(\Gamma_0(N)\)-optimal |
| 5328.k2 | 5328u2 | \([0, 0, 0, -3360, -72592]\) | \(1404928000/50653\) | \(151249047552\) | \([]\) | \(4320\) | \(0.91523\) | |
| 5328.k1 | 5328u3 | \([0, 0, 0, -269760, -53928016]\) | \(727057727488000/37\) | \(110481408\) | \([]\) | \(12960\) | \(1.4645\) |
Rank
sage: E.rank()
The elliptic curves in class 5328u have rank \(0\).
Complex multiplication
The elliptic curves in class 5328u do not have complex multiplication.Modular form 5328.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
