Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 3120o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3120.a4 | 3120o1 | \([0, -1, 0, -4616, -197904]\) | \(-2656166199049/2658140160\) | \(-10887742095360\) | \([2]\) | \(7680\) | \(1.1973\) | \(\Gamma_0(N)\)-optimal |
| 3120.a3 | 3120o2 | \([0, -1, 0, -86536, -9766160]\) | \(17496824387403529/6580454400\) | \(26953541222400\) | \([2, 2]\) | \(15360\) | \(1.5438\) | |
| 3120.a1 | 3120o3 | \([0, -1, 0, -1384456, -626537744]\) | \(71647584155243142409/10140000\) | \(41533440000\) | \([2]\) | \(30720\) | \(1.8904\) | |
| 3120.a2 | 3120o4 | \([0, -1, 0, -99336, -6673680]\) | \(26465989780414729/10571870144160\) | \(43302380110479360\) | \([2]\) | \(30720\) | \(1.8904\) |
Rank
sage: E.rank()
The elliptic curves in class 3120o have rank \(0\).
Complex multiplication
The elliptic curves in class 3120o do not have complex multiplication.Modular form 3120.2.a.o
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.
