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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 6192.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6192.n1 | 6192o2 | \([0, 0, 0, -8625747, -9752021998]\) | \(-23769846831649063249/3261823333284\) | \(-9739752284012691456\) | \([]\) | \(225792\) | \(2.6614\) | |
6192.n2 | 6192o1 | \([0, 0, 0, 22893, 2978642]\) | \(444369620591/1540767744\) | \(-4600707831300096\) | \([]\) | \(32256\) | \(1.6884\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6192.n have rank \(1\).
Complex multiplication
The elliptic curves in class 6192.n do not have complex multiplication.Modular form 6192.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.