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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 9576.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.u1 | 9576d2 | \([0, 0, 0, -118179, -5423490]\) | \(4528177054182/2305248169\) | \(92926361006954496\) | \([2]\) | \(73728\) | \(1.9483\) | |
| 9576.u2 | 9576d1 | \([0, 0, 0, -65259, 6356502]\) | \(1524943337004/16468459\) | \(331928246780928\) | \([2]\) | \(36864\) | \(1.6017\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9576.u have rank \(0\).
Complex multiplication
The elliptic curves in class 9576.u do not have complex multiplication.Modular form 9576.2.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.
