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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 424536.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424536.h1 | 424536h4 | \([0, -1, 0, -57176744, -138074633556]\) | \(1823652903746/328593657\) | \(3724765824353030027741184\) | \([2]\) | \(88473600\) | \(3.4338\) | |
424536.h2 | 424536h2 | \([0, -1, 0, -16845824, 24620297724]\) | \(93280467172/7800849\) | \(44213172009188403078144\) | \([2, 2]\) | \(44236800\) | \(3.0872\) | |
424536.h3 | 424536h1 | \([0, -1, 0, -16492044, 25783950900]\) | \(350104249168/2793\) | \(3957498389651665152\) | \([2]\) | \(22118400\) | \(2.7406\) | \(\Gamma_0(N)\)-optimal* |
424536.h4 | 424536h3 | \([0, -1, 0, 17824616, 112835765260]\) | \(55251546334/517244049\) | \(-5863207994198086595954688\) | \([2]\) | \(88473600\) | \(3.4338\) |
Rank
sage: E.rank()
The elliptic curves in class 424536.h have rank \(1\).
Complex multiplication
The elliptic curves in class 424536.h do not have complex multiplication.Modular form 424536.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.