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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 190608.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190608.u1 | 190608bs2 | \([0, -1, 0, -944335688, 11169917427696]\) | \(-1338795256993539625/20699712\) | \(-1439968721643701010432\) | \([]\) | \(35458560\) | \(3.6081\) | |
| 190608.u2 | 190608bs1 | \([0, -1, 0, -10962968, 17233470960]\) | \(-2094688437625/631351908\) | \(-43919789795629597605888\) | \([]\) | \(11819520\) | \(3.0588\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190608.u have rank \(1\).
Complex multiplication
The elliptic curves in class 190608.u do not have complex multiplication.Modular form 190608.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
