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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 6160k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6160.n4 | 6160k1 | \([0, -1, 0, 160, -6400]\) | \(109902239/4312000\) | \(-17661952000\) | \([2]\) | \(4608\) | \(0.64608\) | \(\Gamma_0(N)\)-optimal |
6160.n2 | 6160k2 | \([0, -1, 0, -4320, -103168]\) | \(2177286259681/105875000\) | \(433664000000\) | \([2]\) | \(9216\) | \(0.99266\) | |
6160.n3 | 6160k3 | \([0, -1, 0, -1440, 174080]\) | \(-80677568161/3131816380\) | \(-12827919892480\) | \([2]\) | \(13824\) | \(1.1954\) | |
6160.n1 | 6160k4 | \([0, -1, 0, -56320, 5135232]\) | \(4823468134087681/30382271150\) | \(124445782630400\) | \([2]\) | \(27648\) | \(1.5420\) |
Rank
sage: E.rank()
The elliptic curves in class 6160k have rank \(0\).
Complex multiplication
The elliptic curves in class 6160k do not have complex multiplication.Modular form 6160.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.