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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 14490h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.f2 | 14490h1 | \([1, -1, 0, -75195, 3656421]\) | \(64500981545311921/29485596672000\) | \(21494999973888000\) | \([2]\) | \(138240\) | \(1.8288\) | \(\Gamma_0(N)\)-optimal |
14490.f1 | 14490h2 | \([1, -1, 0, -605115, -178530075]\) | \(33613237452390629041/532385784000000\) | \(388109236536000000\) | \([2]\) | \(276480\) | \(2.1754\) |
Rank
sage: E.rank()
The elliptic curves in class 14490h have rank \(0\).
Complex multiplication
The elliptic curves in class 14490h do not have complex multiplication.Modular form 14490.2.a.h
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.