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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 392784u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 392784.u2 | 392784u1 | \([0, -1, 0, -39608, -3741072]\) | \(-14260515625/4382748\) | \(-2112003766075392\) | \([2]\) | \(1769472\) | \(1.6542\) | \(\Gamma_0(N)\)-optimal |
| 392784.u1 | 392784u2 | \([0, -1, 0, -674648, -213050256]\) | \(70470585447625/4518018\) | \(2177189067497472\) | \([2]\) | \(3538944\) | \(2.0008\) |
Rank
sage: E.rank()
The elliptic curves in class 392784u have rank \(0\).
Complex multiplication
The elliptic curves in class 392784u do not have complex multiplication.Modular form 392784.2.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.
