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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 80850.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80850.n1 | 80850h4 | \([1, 1, 0, -2245309875, 40947166342125]\) | \(680995599504466943307169/52207031250000000\) | \(95970390930175781250000000\) | \([2]\) | \(61931520\) | \(4.0337\) | |
| 80850.n2 | 80850h2 | \([1, 1, 0, -149677875, 549668278125]\) | \(201738262891771037089/45727545600000000\) | \(84059375192100000000000000\) | \([2, 2]\) | \(30965760\) | \(3.6872\) | |
| 80850.n3 | 80850h1 | \([1, 1, 0, -49325875, -126001737875]\) | \(7220044159551112609/448454983680000\) | \(824379380858880000000000\) | \([2]\) | \(15482880\) | \(3.3406\) | \(\Gamma_0(N)\)-optimal |
| 80850.n4 | 80850h3 | \([1, 1, 0, 340322125, 3397058278125]\) | \(2371297246710590562911/4084000833203280000\) | \(-7507478344148948261250000000\) | \([2]\) | \(61931520\) | \(4.0337\) |
Rank
sage: E.rank()
The elliptic curves in class 80850.n have rank \(0\).
Complex multiplication
The elliptic curves in class 80850.n do not have complex multiplication.Modular form 80850.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
