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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 103488.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.w1 | 103488bb4 | \([0, -1, 0, -459489, -119613087]\) | \(347873904937/395307\) | \(12191655065812992\) | \([2]\) | \(884736\) | \(2.0000\) | |
| 103488.w2 | 103488bb2 | \([0, -1, 0, -36129, -818271]\) | \(169112377/88209\) | \(2720451956834304\) | \([2, 2]\) | \(442368\) | \(1.6535\) | |
| 103488.w3 | 103488bb1 | \([0, -1, 0, -20449, 1122913]\) | \(30664297/297\) | \(9159770898432\) | \([2]\) | \(221184\) | \(1.3069\) | \(\Gamma_0(N)\)-optimal |
| 103488.w4 | 103488bb3 | \([0, -1, 0, 136351, -6510111]\) | \(9090072503/5845851\) | \(-180291770593837056\) | \([2]\) | \(884736\) | \(2.0000\) |
Rank
sage: E.rank()
The elliptic curves in class 103488.w have rank \(0\).
Complex multiplication
The elliptic curves in class 103488.w do not have complex multiplication.Modular form 103488.2.a.w
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.
