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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 311696.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.bh1 | 311696bh2 | \([0, -1, 0, -47134864, -124539385408]\) | \(1596005697643892137/5553856\) | \(40300522247028736\) | \([]\) | \(14100480\) | \(2.8296\) | |
311696.bh2 | 311696bh1 | \([0, -1, 0, -603104, -157541888]\) | \(3343374301177/453439756\) | \(3290301184324059136\) | \([]\) | \(4700160\) | \(2.2803\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 311696.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 311696.bh do not have complex multiplication.Modular form 311696.2.a.bh
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.