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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 47040u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47040.bu2 | 47040u1 | \([0, -1, 0, -2501, 47685]\) | \(4927700992/151875\) | \(53343360000\) | \([2]\) | \(61440\) | \(0.83395\) | \(\Gamma_0(N)\)-optimal |
| 47040.bu1 | 47040u2 | \([0, -1, 0, -6001, -111215]\) | \(4253563312/1476225\) | \(8295959347200\) | \([2]\) | \(122880\) | \(1.1805\) |
Rank
sage: E.rank()
The elliptic curves in class 47040u have rank \(0\).
Complex multiplication
The elliptic curves in class 47040u do not have complex multiplication.Modular form 47040.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
