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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 140679u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 140679.u1 | 140679u1 | \([0, 0, 1, -27930, 2707213]\) | \(-28094464000/20657483\) | \(-1771712186533443\) | \([]\) | \(483840\) | \(1.6253\) | \(\Gamma_0(N)\)-optimal |
| 140679.u2 | 140679u2 | \([0, 0, 1, 227850, -41785718]\) | \(15252992000000/17621717267\) | \(-1511346335349311307\) | \([]\) | \(1451520\) | \(2.1746\) |
Rank
sage: E.rank()
The elliptic curves in class 140679u have rank \(0\).
Complex multiplication
The elliptic curves in class 140679u do not have complex multiplication.Modular form 140679.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
