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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 130130k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130130.k2 | 130130k1 | \([1, 0, 1, 20107, 2003328]\) | \(186267240431/466385920\) | \(-2251155756129280\) | \([2]\) | \(860160\) | \(1.6297\) | \(\Gamma_0(N)\)-optimal |
130130.k1 | 130130k2 | \([1, 0, 1, -169173, 22369856]\) | \(110931033861649/19352933600\) | \(93412914076882400\) | \([2]\) | \(1720320\) | \(1.9762\) |
Rank
sage: E.rank()
The elliptic curves in class 130130k have rank \(0\).
Complex multiplication
The elliptic curves in class 130130k do not have complex multiplication.Modular form 130130.2.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 Cremona 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 Cremona labels.