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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 155526bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.s2 | 155526bt1 | \([1, 0, 1, 453077, -30658078]\) | \(590589719/365148\) | \(-6359517729907899228\) | \([2]\) | \(4866048\) | \(2.2972\) | \(\Gamma_0(N)\)-optimal |
155526.s1 | 155526bt2 | \([1, 0, 1, -1879813, -249949738]\) | \(42180533641/22862322\) | \(398176471200344579442\) | \([2]\) | \(9732096\) | \(2.6437\) |
Rank
sage: E.rank()
The elliptic curves in class 155526bt have rank \(0\).
Complex multiplication
The elliptic curves in class 155526bt do not have complex multiplication.Modular form 155526.2.a.bt
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.