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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 9408.de
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9408.de1 | 9408de2 | \([0, 1, 0, -8801, -312033]\) | \(838561807/26244\) | \(2359739547648\) | \([2]\) | \(24576\) | \(1.1492\) | |
9408.de2 | 9408de1 | \([0, 1, 0, 159, -16353]\) | \(4913/1296\) | \(-116530348032\) | \([2]\) | \(12288\) | \(0.80263\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9408.de have rank \(0\).
Complex multiplication
The elliptic curves in class 9408.de do not have complex multiplication.Modular form 9408.2.a.de
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.