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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 18150h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18150.h2 | 18150h1 | \([1, 1, 0, 981550, -643663500]\) | \(6045109175/13856832\) | \(-239728741745625000000\) | \([]\) | \(777600\) | \(2.5946\) | \(\Gamma_0(N)\)-optimal |
18150.h1 | 18150h2 | \([1, 1, 0, -9227825, 22215127125]\) | \(-5023028944825/9420668928\) | \(-162981344401920000000000\) | \([]\) | \(2332800\) | \(3.1439\) |
Rank
sage: E.rank()
The elliptic curves in class 18150h have rank \(0\).
Complex multiplication
The elliptic curves in class 18150h do not have complex multiplication.Modular form 18150.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.