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SageMath
E = EllipticCurve("fh1")
E.isogeny_class()
Elliptic curves in class 22050fh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.ea2 | 22050fh1 | \([1, -1, 1, -1805, 25197]\) | \(46585/8\) | \(111628125000\) | \([]\) | \(25920\) | \(0.84024\) | \(\Gamma_0(N)\)-optimal |
22050.ea1 | 22050fh2 | \([1, -1, 1, -41180, -3203553]\) | \(553463785/512\) | \(7144200000000\) | \([]\) | \(77760\) | \(1.3895\) |
Rank
sage: E.rank()
The elliptic curves in class 22050fh have rank \(1\).
Complex multiplication
The elliptic curves in class 22050fh do not have complex multiplication.Modular form 22050.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.