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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 4998.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4998.u1 | 4998q2 | \([1, 0, 1, -18695, -985246]\) | \(6141556990297/1019592\) | \(119953979208\) | \([2]\) | \(9216\) | \(1.1339\) | |
| 4998.u2 | 4998q1 | \([1, 0, 1, -1055, -18574]\) | \(-1102302937/616896\) | \(-72577197504\) | \([2]\) | \(4608\) | \(0.78728\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4998.u have rank \(1\).
Complex multiplication
The elliptic curves in class 4998.u do not have complex multiplication.Modular form 4998.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
