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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 166410.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.b1 | 166410bz2 | \([1, -1, 0, -16020, -909104]\) | \(-337335507529/72000000\) | \(-97050312000000\) | \([]\) | \(580608\) | \(1.4052\) | |
166410.b2 | 166410bz1 | \([1, -1, 0, 1395, 6925]\) | \(222641831/145800\) | \(-196526881800\) | \([]\) | \(193536\) | \(0.85585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166410.b have rank \(1\).
Complex multiplication
The elliptic curves in class 166410.b do not have complex multiplication.Modular form 166410.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.