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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 8550b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.q2 | 8550b1 | \([1, -1, 0, -1542, -7884]\) | \(961504803/486400\) | \(205200000000\) | \([2]\) | \(15360\) | \(0.86315\) | \(\Gamma_0(N)\)-optimal |
8550.q1 | 8550b2 | \([1, -1, 0, -13542, 604116]\) | \(651038076963/7220000\) | \(3045937500000\) | \([2]\) | \(30720\) | \(1.2097\) |
Rank
sage: E.rank()
The elliptic curves in class 8550b have rank \(1\).
Complex multiplication
The elliptic curves in class 8550b do not have complex multiplication.Modular form 8550.2.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 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.