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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 465690.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
465690.b1 | 465690b3 | \([1, 1, 0, -10466648756828, 13033451602201390032]\) | \(2695411376533589106170675619466398289/2123546400000000\) | \(99904111232378400000000\) | \([2]\) | \(11094589440\) | \(5.6019\) | \(\Gamma_0(N)\)-optimal* |
465690.b2 | 465690b2 | \([1, 1, 0, -654165551708, 203647473976759248]\) | \(658059431397928037221595991689809/18470704385855324160000\) | \(868970560523127663647784960000\) | \([2, 2]\) | \(5547294720\) | \(5.2554\) | \(\Gamma_0(N)\)-optimal* |
465690.b3 | 465690b4 | \([1, 1, 0, -653333807708, 204191157249309648]\) | \(-655552536799502322424300617353809/3486819805571317382996428800\) | \(-164040509641351334613681412749772800\) | \([2]\) | \(11094589440\) | \(5.6019\) | |
465690.b4 | 465690b1 | \([1, 1, 0, -40937335388, 3173481055933392]\) | \(161272686097343726562556430929/851057913027019721932800\) | \(40038769300377519622703598796800\) | \([2]\) | \(2773647360\) | \(4.9088\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 465690.b have rank \(0\).
Complex multiplication
The elliptic curves in class 465690.b do not have complex multiplication.Modular form 465690.2.a.b
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.