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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 96192.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96192.k1 | 96192n2 | \([0, 0, 0, -184620, -30520496]\) | \(14566408766500/6777027\) | \(323777507033088\) | \([2]\) | \(450560\) | \(1.7405\) | |
| 96192.k2 | 96192n1 | \([0, 0, 0, -9660, -637328]\) | \(-8346562000/9861183\) | \(-117781338636288\) | \([2]\) | \(225280\) | \(1.3939\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96192.k have rank \(1\).
Complex multiplication
The elliptic curves in class 96192.k do not have complex multiplication.Modular form 96192.2.a.k
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.
