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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 24336by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24336.h3 | 24336by1 | \([0, 0, 0, 11661, 795314]\) | \(12167/26\) | \(-374732135571456\) | \([]\) | \(80640\) | \(1.4807\) | \(\Gamma_0(N)\)-optimal |
24336.h2 | 24336by2 | \([0, 0, 0, -110019, -27994174]\) | \(-10218313/17576\) | \(-253318923646304256\) | \([]\) | \(241920\) | \(2.0300\) | |
24336.h1 | 24336by3 | \([0, 0, 0, -11182899, -14393948686]\) | \(-10730978619193/6656\) | \(-95931426706292736\) | \([]\) | \(725760\) | \(2.5793\) |
Rank
sage: E.rank()
The elliptic curves in class 24336by have rank \(1\).
Complex multiplication
The elliptic curves in class 24336by do not have complex multiplication.Modular form 24336.2.a.by
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.