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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 196392u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 196392.h2 | 196392u1 | \([0, -1, 0, -13148, 1016436]\) | \(-8346562000/9861183\) | \(-297000529604352\) | \([2]\) | \(506880\) | \(1.4710\) | \(\Gamma_0(N)\)-optimal |
| 196392.h1 | 196392u2 | \([0, -1, 0, -251288, 48549180]\) | \(14566408766500/6777027\) | \(816445900311552\) | \([2]\) | \(1013760\) | \(1.8176\) |
Rank
sage: E.rank()
The elliptic curves in class 196392u have rank \(1\).
Complex multiplication
The elliptic curves in class 196392u do not have complex multiplication.Modular form 196392.2.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.
