Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 5440l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5440.w2 | 5440l1 | \([0, -1, 0, -163425, 25482977]\) | \(1841373668746009/31443200\) | \(8242646220800\) | \([2]\) | \(30720\) | \(1.6079\) | \(\Gamma_0(N)\)-optimal |
| 5440.w3 | 5440l2 | \([0, -1, 0, -158305, 27149025]\) | \(-1673672305534489/241375690000\) | \(-63275188879360000\) | \([2]\) | \(61440\) | \(1.9545\) | |
| 5440.w1 | 5440l3 | \([0, -1, 0, -266785, -10343775]\) | \(8010684753304969/4456448000000\) | \(1168231104512000000\) | \([2]\) | \(92160\) | \(2.1572\) | |
| 5440.w4 | 5440l4 | \([0, -1, 0, 1043935, -82957663]\) | \(479958568556831351/289000000000000\) | \(-75759616000000000000\) | \([2]\) | \(184320\) | \(2.5038\) |
Rank
sage: E.rank()
The elliptic curves in class 5440l have rank \(1\).
Complex multiplication
The elliptic curves in class 5440l do not have complex multiplication.Modular form 5440.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
