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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 229320.du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.du1 | 229320cz2 | \([0, 0, 0, -141267, -20140274]\) | \(1775007362/29575\) | \(5194819642521600\) | \([2]\) | \(1474560\) | \(1.8140\) | |
| 229320.du2 | 229320cz1 | \([0, 0, 0, -17787, 431494]\) | \(7086244/3185\) | \(279721057674240\) | \([2]\) | \(737280\) | \(1.4674\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 229320.du have rank \(1\).
Complex multiplication
The elliptic curves in class 229320.du do not have complex multiplication.Modular form 229320.2.a.du
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.
