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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 18240bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18240.bu4 | 18240bh1 | \([0, 1, 0, 79, 495]\) | \(3286064/7695\) | \(-126074880\) | \([2]\) | \(6144\) | \(0.23837\) | \(\Gamma_0(N)\)-optimal |
18240.bu3 | 18240bh2 | \([0, 1, 0, -641, 4959]\) | \(445138564/81225\) | \(5323161600\) | \([2, 2]\) | \(12288\) | \(0.58494\) | |
18240.bu2 | 18240bh3 | \([0, 1, 0, -3041, -60801]\) | \(23735908082/1954815\) | \(256221511680\) | \([2]\) | \(24576\) | \(0.93152\) | |
18240.bu1 | 18240bh4 | \([0, 1, 0, -9761, 367935]\) | \(784767874322/35625\) | \(4669440000\) | \([2]\) | \(24576\) | \(0.93152\) |
Rank
sage: E.rank()
The elliptic curves in class 18240bh have rank \(1\).
Complex multiplication
The elliptic curves in class 18240bh do not have complex multiplication.Modular form 18240.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.