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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 37440.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.du1 | 37440ce2 | \([0, 0, 0, -7212, -232144]\) | \(434163602/7605\) | \(726669066240\) | \([2]\) | \(49152\) | \(1.0725\) | |
37440.du2 | 37440ce1 | \([0, 0, 0, -12, -10384]\) | \(-4/975\) | \(-46581350400\) | \([2]\) | \(24576\) | \(0.72592\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37440.du have rank \(1\).
Complex multiplication
The elliptic curves in class 37440.du do not have complex multiplication.Modular form 37440.2.a.du
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.