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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 193600j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.w2 | 193600j1 | \([0, 1, 0, 141167, -31995537]\) | \(5488/11\) | \(-623589472000000000\) | \([2]\) | \(3072000\) | \(2.0990\) | \(\Gamma_0(N)\)-optimal |
193600.w1 | 193600j2 | \([0, 1, 0, -1068833, -342965537]\) | \(595508/121\) | \(27437936768000000000\) | \([2]\) | \(6144000\) | \(2.4456\) |
Rank
sage: E.rank()
The elliptic curves in class 193600j have rank \(0\).
Complex multiplication
The elliptic curves in class 193600j do not have complex multiplication.Modular form 193600.2.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 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.