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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 308550fh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.fh1 | 308550fh1 | \([1, 1, 1, -2734663, -1728001219]\) | \(81706955619457/744505344\) | \(20608384870656000000\) | \([2]\) | \(17203200\) | \(2.5282\) | \(\Gamma_0(N)\)-optimal |
308550.fh2 | 308550fh2 | \([1, 1, 1, -798663, -4124769219]\) | \(-2035346265217/264305213568\) | \(-7316137632089682000000\) | \([2]\) | \(34406400\) | \(2.8748\) |
Rank
sage: E.rank()
The elliptic curves in class 308550fh have rank \(1\).
Complex multiplication
The elliptic curves in class 308550fh do not have complex multiplication.Modular form 308550.2.a.fh
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.