Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 5440.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5440.n1 | 5440h3 | \([0, 0, 0, -4652, -119504]\) | \(84944038338/2088025\) | \(273681612800\) | \([2]\) | \(4096\) | \(0.97844\) | |
5440.n2 | 5440h2 | \([0, 0, 0, -652, 3696]\) | \(467720676/180625\) | \(11837440000\) | \([2, 2]\) | \(2048\) | \(0.63186\) | |
5440.n3 | 5440h1 | \([0, 0, 0, -572, 5264]\) | \(1263257424/425\) | \(6963200\) | \([2]\) | \(1024\) | \(0.28529\) | \(\Gamma_0(N)\)-optimal |
5440.n4 | 5440h4 | \([0, 0, 0, 2068, 26544]\) | \(7462174302/6640625\) | \(-870400000000\) | \([4]\) | \(4096\) | \(0.97844\) |
Rank
sage: E.rank()
The elliptic curves in class 5440.n have rank \(1\).
Complex multiplication
The elliptic curves in class 5440.n do not have complex multiplication.Modular form 5440.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.