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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 33600.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.b1 | 33600eu2 | \([0, -1, 0, -137033, -19479063]\) | \(4446542056384/25725\) | \(1646400000000\) | \([2]\) | \(184320\) | \(1.5345\) | |
33600.b2 | 33600eu1 | \([0, -1, 0, -8408, -313938]\) | \(-65743598656/5294205\) | \(-5294205000000\) | \([2]\) | \(92160\) | \(1.1879\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33600.b have rank \(0\).
Complex multiplication
The elliptic curves in class 33600.b do not have complex multiplication.Modular form 33600.2.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.