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SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 87120.ds
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
87120.ds1 | 87120ck2 | \([0, 0, 0, -257367, -50213306]\) | \(5702413264/5445\) | \(1800203031348480\) | \([2]\) | \(491520\) | \(1.8488\) | |
87120.ds2 | 87120ck1 | \([0, 0, 0, -12342, -1159301]\) | \(-10061824/22275\) | \(-460279184151600\) | \([2]\) | \(245760\) | \(1.5023\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.ds have rank \(0\).
Complex multiplication
The elliptic curves in class 87120.ds do not have complex multiplication.Modular form 87120.2.a.ds
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.