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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 129600bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129600.cy3 | 129600bh1 | \([0, 0, 0, -7500, 262000]\) | \(-140625/8\) | \(-2654208000000\) | \([]\) | \(165888\) | \(1.1409\) | \(\Gamma_0(N)\)-optimal |
129600.cy4 | 129600bh2 | \([0, 0, 0, 40500, 486000]\) | \(3375/2\) | \(-4353564672000000\) | \([]\) | \(497664\) | \(1.6902\) | |
129600.cy2 | 129600bh3 | \([0, 0, 0, -151500, -46106000]\) | \(-1159088625/2097152\) | \(-695784701952000000\) | \([]\) | \(1161216\) | \(2.1138\) | |
129600.cy1 | 129600bh4 | \([0, 0, 0, -15511500, -23514138000]\) | \(-189613868625/128\) | \(-278628139008000000\) | \([]\) | \(3483648\) | \(2.6631\) |
Rank
sage: E.rank()
The elliptic curves in class 129600bh have rank \(1\).
Complex multiplication
The elliptic curves in class 129600bh do not have complex multiplication.Modular form 129600.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.