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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 29400.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29400.bh1 | 29400ba2 | \([0, -1, 0, -74888, -7849428]\) | \(4496182/9\) | \(92974710528000\) | \([2]\) | \(100352\) | \(1.5676\) | |
29400.bh2 | 29400ba1 | \([0, -1, 0, -6288, -29028]\) | \(5324/3\) | \(15495785088000\) | \([2]\) | \(50176\) | \(1.2210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29400.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 29400.bh do not have complex multiplication.Modular form 29400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.