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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 6006.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6006.n1 | 6006p4 | \([1, 0, 1, -57751, -5341630]\) | \(21300579951997515625/22665575244312\) | \(22665575244312\) | \([2]\) | \(27648\) | \(1.4792\) | |
| 6006.n2 | 6006p3 | \([1, 0, 1, -4511, -38926]\) | \(10148545224987625/5231008630848\) | \(5231008630848\) | \([2]\) | \(13824\) | \(1.1326\) | |
| 6006.n3 | 6006p2 | \([1, 0, 1, -2626, 43862]\) | \(2001566936265625/318878437878\) | \(318878437878\) | \([6]\) | \(9216\) | \(0.92985\) | |
| 6006.n4 | 6006p1 | \([1, 0, 1, -2516, 48350]\) | \(1760384222493625/58270212\) | \(58270212\) | \([6]\) | \(4608\) | \(0.58328\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6006.n have rank \(0\).
Complex multiplication
The elliptic curves in class 6006.n do not have complex multiplication.Modular form 6006.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
