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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 9360bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.bc4 | 9360bz1 | \([0, 0, 0, -41547, 5384954]\) | \(-2656166199049/2658140160\) | \(-7937163987517440\) | \([2]\) | \(61440\) | \(1.7466\) | \(\Gamma_0(N)\)-optimal |
| 9360.bc3 | 9360bz2 | \([0, 0, 0, -778827, 264465146]\) | \(17496824387403529/6580454400\) | \(19649131551129600\) | \([2, 2]\) | \(122880\) | \(2.0931\) | |
| 9360.bc2 | 9360bz3 | \([0, 0, 0, -894027, 181083386]\) | \(26465989780414729/10571870144160\) | \(31567435100539453440\) | \([2]\) | \(245760\) | \(2.4397\) | |
| 9360.bc1 | 9360bz4 | \([0, 0, 0, -12460107, 16928979194]\) | \(71647584155243142409/10140000\) | \(30277877760000\) | \([4]\) | \(245760\) | \(2.4397\) |
Rank
sage: E.rank()
The elliptic curves in class 9360bz have rank \(0\).
Complex multiplication
The elliptic curves in class 9360bz do not have complex multiplication.Modular form 9360.2.a.bz
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.
