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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 14490n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.l4 | 14490n1 | \([1, -1, 0, 2595420, -2925690800]\) | \(2652277923951208297919/6605028468326400000\) | \(-4815065753409945600000\) | \([2]\) | \(1228800\) | \(2.8443\) | \(\Gamma_0(N)\)-optimal |
| 14490.l3 | 14490n2 | \([1, -1, 0, -21780900, -32669676464]\) | \(1567558142704512417614401/274462175610000000000\) | \(200082926019690000000000\) | \([2, 2]\) | \(2457600\) | \(3.1909\) | |
| 14490.l1 | 14490n3 | \([1, -1, 0, -332280900, -2331176976464]\) | \(5565604209893236690185614401/229307220930246900000\) | \(167164964058149990100000\) | \([2]\) | \(4915200\) | \(3.5375\) | |
| 14490.l2 | 14490n4 | \([1, -1, 0, -101302020, 361930025200]\) | \(157706830105239346386477121/13650704956054687500000\) | \(9951363912963867187500000\) | \([2]\) | \(4915200\) | \(3.5375\) |
Rank
sage: E.rank()
The elliptic curves in class 14490n have rank \(1\).
Complex multiplication
The elliptic curves in class 14490n do not have complex multiplication.Modular form 14490.2.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 Cremona 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 Cremona labels.
