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SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 193600fw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.r2 | 193600fw1 | \([0, 1, 0, 5647, 258223]\) | \(5488/11\) | \(-39909726208000\) | \([2]\) | \(614400\) | \(1.2943\) | \(\Gamma_0(N)\)-optimal |
193600.r1 | 193600fw2 | \([0, 1, 0, -42753, 2726623]\) | \(595508/121\) | \(1756027953152000\) | \([2]\) | \(1228800\) | \(1.6408\) |
Rank
sage: E.rank()
The elliptic curves in class 193600fw have rank \(1\).
Complex multiplication
The elliptic curves in class 193600fw do not have complex multiplication.Modular form 193600.2.a.fw
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.