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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 4368.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4368.u1 | 4368x2 | \([0, 1, 0, -6228, -191160]\) | \(104375673106000/69854967\) | \(17882871552\) | \([2]\) | \(3840\) | \(0.90583\) | |
| 4368.u2 | 4368x1 | \([0, 1, 0, -313, -4246]\) | \(-212629504000/340075827\) | \(-5441213232\) | \([2]\) | \(1920\) | \(0.55926\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4368.u have rank \(0\).
Complex multiplication
The elliptic curves in class 4368.u do not have complex multiplication.Modular form 4368.2.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.
