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SageMath
E = EllipticCurve("of1")
E.isogeny_class()
Elliptic curves in class 158400of
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.k1 | 158400of1 | \([0, 0, 0, -240300, 45198000]\) | \(76136652/275\) | \(5542732800000000\) | \([2]\) | \(1474560\) | \(1.8820\) | \(\Gamma_0(N)\)-optimal |
158400.k2 | 158400of2 | \([0, 0, 0, -132300, 86022000]\) | \(-6353046/75625\) | \(-3048503040000000000\) | \([2]\) | \(2949120\) | \(2.2286\) |
Rank
sage: E.rank()
The elliptic curves in class 158400of have rank \(1\).
Complex multiplication
The elliptic curves in class 158400of do not have complex multiplication.Modular form 158400.2.a.of
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.