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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 38640.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38640.e1 | 38640bl1 | \([0, -1, 0, -341, -7395]\) | \(-1073741824/5325075\) | \(-21811507200\) | \([]\) | \(31104\) | \(0.66824\) | \(\Gamma_0(N)\)-optimal |
38640.e2 | 38640bl2 | \([0, -1, 0, 3019, 182781]\) | \(742692847616/3992296875\) | \(-16352448000000\) | \([]\) | \(93312\) | \(1.2175\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.e have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.e do not have complex multiplication.Modular form 38640.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.