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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 528b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 528.b4 | 528b1 | \([0, -1, 0, 1, -6]\) | \(2048/891\) | \(-14256\) | \([2]\) | \(48\) | \(-0.52383\) | \(\Gamma_0(N)\)-optimal |
| 528.b3 | 528b2 | \([0, -1, 0, -44, -96]\) | \(37642192/1089\) | \(278784\) | \([2, 2]\) | \(96\) | \(-0.17725\) | |
| 528.b1 | 528b3 | \([0, -1, 0, -704, -6960]\) | \(37736227588/33\) | \(33792\) | \([2]\) | \(192\) | \(0.16932\) | |
| 528.b2 | 528b4 | \([0, -1, 0, -104, 288]\) | \(122657188/43923\) | \(44977152\) | \([4]\) | \(192\) | \(0.16932\) |
Rank
sage: E.rank()
The elliptic curves in class 528b have rank \(0\).
Complex multiplication
The elliptic curves in class 528b do not have complex multiplication.Modular form 528.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
