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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5733.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5733.b1 | 5733b1 | \([1, -1, 1, -230, -1004]\) | \(421875/91\) | \(289063593\) | \([2]\) | \(1536\) | \(0.33756\) | \(\Gamma_0(N)\)-optimal |
5733.b2 | 5733b2 | \([1, -1, 1, 505, -6590]\) | \(4492125/8281\) | \(-26304786963\) | \([2]\) | \(3072\) | \(0.68413\) |
Rank
sage: E.rank()
The elliptic curves in class 5733.b have rank \(1\).
Complex multiplication
The elliptic curves in class 5733.b do not have complex multiplication.Modular form 5733.2.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.