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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 457776bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.bh1 | 457776bh1 | \([0, 0, 0, -375411, -42988750]\) | \(81182737/35904\) | \(2587759072080297984\) | \([2]\) | \(5308416\) | \(2.2288\) | \(\Gamma_0(N)\)-optimal |
457776.bh2 | 457776bh2 | \([0, 0, 0, 1289229, -320317774]\) | \(3288008303/2517768\) | \(-181466604929630896128\) | \([2]\) | \(10616832\) | \(2.5754\) |
Rank
sage: E.rank()
The elliptic curves in class 457776bh have rank \(1\).
Complex multiplication
The elliptic curves in class 457776bh do not have complex multiplication.Modular form 457776.2.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 Cremona 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 Cremona labels.