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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 388080u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.u1 | 388080u1 | \([0, 0, 0, -1365483, 611337818]\) | \(2336752783/12375\) | \(1491128407448064000\) | \([2]\) | \(6881280\) | \(2.3319\) | \(\Gamma_0(N)\)-optimal |
| 388080.u2 | 388080u2 | \([0, 0, 0, -624603, 1272054602]\) | \(-223648543/5671875\) | \(-683433853413696000000\) | \([2]\) | \(13762560\) | \(2.6784\) |
Rank
sage: E.rank()
The elliptic curves in class 388080u have rank \(0\).
Complex multiplication
The elliptic curves in class 388080u do not have complex multiplication.Modular form 388080.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
