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SageMath
E = EllipticCurve("ku1")
E.isogeny_class()
Elliptic curves in class 141120.ku
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.ku1 | 141120od2 | \([0, 0, 0, -1033452, -404372304]\) | \(68971442301/400\) | \(707921864294400\) | \([2]\) | \(1179648\) | \(2.0397\) | |
141120.ku2 | 141120od1 | \([0, 0, 0, -65772, -6075216]\) | \(17779581/1280\) | \(2265349965742080\) | \([2]\) | \(589824\) | \(1.6931\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.ku have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.ku do not have complex multiplication.Modular form 141120.2.a.ku
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.