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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 284592eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.eo4 | 284592eo1 | \([0, -1, 0, 330048, 44359680]\) | \(4657463/3696\) | \(-3155268062449434624\) | \([2]\) | \(4423680\) | \(2.2376\) | \(\Gamma_0(N)\)-optimal |
284592.eo3 | 284592eo2 | \([0, -1, 0, -1567232, 385870080]\) | \(498677257/213444\) | \(182216730606454849536\) | \([2, 2]\) | \(8847360\) | \(2.5841\) | |
284592.eo1 | 284592eo3 | \([0, -1, 0, -21488672, 38332228992]\) | \(1285429208617/614922\) | \(524957723890024685568\) | \([2]\) | \(17694720\) | \(2.9307\) | |
284592.eo2 | 284592eo4 | \([0, -1, 0, -12002272, -15734179712]\) | \(223980311017/4278582\) | \(3652617190793026756608\) | \([2]\) | \(17694720\) | \(2.9307\) |
Rank
sage: E.rank()
The elliptic curves in class 284592eo have rank \(0\).
Complex multiplication
The elliptic curves in class 284592eo do not have complex multiplication.Modular form 284592.2.a.eo
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.