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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 115920.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.k1 | 115920dd2 | \([0, 0, 0, -3617283, -1925328382]\) | \(1753007192038126081/478174101507200\) | \(1427820216314875084800\) | \([2]\) | \(5160960\) | \(2.7670\) | |
| 115920.k2 | 115920dd1 | \([0, 0, 0, -1313283, 555158018]\) | \(83890194895342081/3958384640000\) | \(11819673200885760000\) | \([2]\) | \(2580480\) | \(2.4204\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.k have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.k do not have complex multiplication.Modular form 115920.2.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.
