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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 184093.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
184093.j1 | 184093j3 | \([0, 1, 1, -1661557, 2031201785]\) | \(-178643795968/524596891\) | \(-1489729715863913531371\) | \([]\) | \(7962624\) | \(2.7497\) | |
184093.j2 | 184093j1 | \([0, 1, 1, -103847, -12938565]\) | \(-43614208/91\) | \(-258418237830571\) | \([]\) | \(884736\) | \(1.6511\) | \(\Gamma_0(N)\)-optimal |
184093.j3 | 184093j2 | \([0, 1, 1, 179373, -63960648]\) | \(224755712/753571\) | \(-2139961427474958451\) | \([]\) | \(2654208\) | \(2.2004\) |
Rank
sage: E.rank()
The elliptic curves in class 184093.j have rank \(0\).
Complex multiplication
The elliptic curves in class 184093.j do not have complex multiplication.Modular form 184093.2.a.j
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.