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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 33462.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33462.b1 | 33462p2 | \([1, -1, 0, -636, -4042]\) | \(8560539/2662\) | \(8854948674\) | \([]\) | \(24192\) | \(0.61309\) | |
33462.b2 | 33462p1 | \([1, -1, 0, -246, 1548]\) | \(361635651/88\) | \(401544\) | \([]\) | \(8064\) | \(0.063782\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33462.b have rank \(2\).
Complex multiplication
The elliptic curves in class 33462.b do not have complex multiplication.Modular form 33462.2.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.