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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 8880.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8880.bb1 | 8880i3 | \([0, 1, 0, -5328000, -4735407852]\) | \(8167450100737631904002/124875\) | \(255744000\) | \([2]\) | \(101376\) | \(2.0928\) | |
| 8880.bb2 | 8880i4 | \([0, 1, 0, -338000, -71739852]\) | \(2085187657182084002/124500749500125\) | \(254977534976256000\) | \([4]\) | \(101376\) | \(2.0928\) | |
| 8880.bb3 | 8880i2 | \([0, 1, 0, -333000, -74073852]\) | \(3988023972023988004/15593765625\) | \(15968016000000\) | \([2, 2]\) | \(50688\) | \(1.7462\) | |
| 8880.bb4 | 8880i1 | \([0, 1, 0, -20500, -1198852]\) | \(-3721915550952016/243896484375\) | \(-62437500000000\) | \([2]\) | \(25344\) | \(1.3997\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8880.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 8880.bb do not have complex multiplication.Modular form 8880.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
