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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 162624.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162624.b1 | 162624bz2 | \([0, -1, 0, -1169505, 418883841]\) | \(286191179/43218\) | \(26713989659921743872\) | \([2]\) | \(6488064\) | \(2.4517\) | |
162624.b2 | 162624bz1 | \([0, -1, 0, -317665, -62405759]\) | \(5735339/588\) | \(363455641631588352\) | \([2]\) | \(3244032\) | \(2.1051\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162624.b have rank \(0\).
Complex multiplication
The elliptic curves in class 162624.b do not have complex multiplication.Modular form 162624.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.