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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 450800.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.h1 | 450800h1 | \([0, 1, 0, -294408, -100428812]\) | \(-7649089/7360\) | \(-2715451863040000000\) | \([]\) | \(8709120\) | \(2.2333\) | \(\Gamma_0(N)\)-optimal* |
450800.h2 | 450800h2 | \([0, 1, 0, 2449592, 1738051188]\) | \(4405959551/6083500\) | \(-2244490680544000000000\) | \([]\) | \(26127360\) | \(2.7826\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800.h have rank \(2\).
Complex multiplication
The elliptic curves in class 450800.h do not have complex multiplication.Modular form 450800.2.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 LMFDB 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 LMFDB labels.