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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 19074bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19074.bd4 | 19074bh1 | \([1, 0, 0, -584, 48]\) | \(912673/528\) | \(12744636432\) | \([2]\) | \(20480\) | \(0.62851\) | \(\Gamma_0(N)\)-optimal |
19074.bd2 | 19074bh2 | \([1, 0, 0, -6364, -195316]\) | \(1180932193/4356\) | \(105143250564\) | \([2, 2]\) | \(40960\) | \(0.97508\) | |
19074.bd1 | 19074bh3 | \([1, 0, 0, -101734, -12498046]\) | \(4824238966273/66\) | \(1593079554\) | \([2]\) | \(81920\) | \(1.3217\) | |
19074.bd3 | 19074bh4 | \([1, 0, 0, -3474, -372762]\) | \(-192100033/2371842\) | \(-57250499932098\) | \([2]\) | \(81920\) | \(1.3217\) |
Rank
sage: E.rank()
The elliptic curves in class 19074bh have rank \(0\).
Complex multiplication
The elliptic curves in class 19074bh do not have complex multiplication.Modular form 19074.2.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.