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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 179520.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.u1 | 179520dy4 | \([0, -1, 0, -43681, -3499199]\) | \(70323656654162/3733455\) | \(489351413760\) | \([2]\) | \(524288\) | \(1.3108\) | |
| 179520.u2 | 179520dy2 | \([0, -1, 0, -2881, -47519]\) | \(40366797124/7868025\) | \(515638886400\) | \([2, 2]\) | \(262144\) | \(0.96422\) | |
| 179520.u3 | 179520dy1 | \([0, -1, 0, -881, 9681]\) | \(4620876496/350625\) | \(5744640000\) | \([2]\) | \(131072\) | \(0.61764\) | \(\Gamma_0(N)\)-optimal |
| 179520.u4 | 179520dy3 | \([0, -1, 0, 5919, -288639]\) | \(174938513038/372086055\) | \(-48770063400960\) | \([2]\) | \(524288\) | \(1.3108\) |
Rank
sage: E.rank()
The elliptic curves in class 179520.u have rank \(2\).
Complex multiplication
The elliptic curves in class 179520.u do not have complex multiplication.Modular form 179520.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
