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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 486720.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.u1 | 486720u3 | \([0, 0, 0, -2922348, 1922849552]\) | \(23937672968/45\) | \(5188598800220160\) | \([2]\) | \(9437184\) | \(2.2707\) | \(\Gamma_0(N)\)-optimal* |
486720.u2 | 486720u4 | \([0, 0, 0, -488748, -92414608]\) | \(111980168/32805\) | \(3782488525360496640\) | \([2]\) | \(9437184\) | \(2.2707\) | |
486720.u3 | 486720u2 | \([0, 0, 0, -184548, 29387072]\) | \(48228544/2025\) | \(29185868251238400\) | \([2, 2]\) | \(4718592\) | \(1.9241\) | \(\Gamma_0(N)\)-optimal* |
486720.u4 | 486720u1 | \([0, 0, 0, 5577, 1704872]\) | \(85184/5625\) | \(-1266747753960000\) | \([2]\) | \(2359296\) | \(1.5775\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 486720.u have rank \(1\).
Complex multiplication
The elliptic curves in class 486720.u do not have complex multiplication.Modular form 486720.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.