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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 115920.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115920.bh1 | 115920dl2 | \([0, 0, 0, -573123, 166896322]\) | \(6972359126281921/5071500000\) | \(15143417856000000\) | \([2]\) | \(1474560\) | \(2.0393\) | |
115920.bh2 | 115920dl1 | \([0, 0, 0, -43203, 1455298]\) | \(2986606123201/1421952000\) | \(4245925920768000\) | \([2]\) | \(737280\) | \(1.6927\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.bh have rank \(2\).
Complex multiplication
The elliptic curves in class 115920.bh do not have complex multiplication.Modular form 115920.2.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.