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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 43890.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43890.k1 | 43890k2 | \([1, 1, 0, -2632, -52136]\) | \(2017619016383881/42244125000\) | \(42244125000\) | \([2]\) | \(64512\) | \(0.82868\) | |
43890.k2 | 43890k1 | \([1, 1, 0, -352, 1216]\) | \(4844824797961/2001384000\) | \(2001384000\) | \([2]\) | \(32256\) | \(0.48211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43890.k have rank \(1\).
Complex multiplication
The elliptic curves in class 43890.k do not have complex multiplication.Modular form 43890.2.a.k
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.