Elliptic Curve Isogeny Class with LMFDB label 441.f (Cremona label 441c)

• Label: 441.f
• Number of curves: 6
• Conductor: 441
• CM: no
• Rank: 1

Elliptic curves in class 441.f

LMFDB label	Cremona label	Weierstrass coefficients	Torsion order	Modular degree	Optimality
441.f1	441c5	[1, -1, 0, -345753, -78165914]	2	1536
441.f2	441c3	[1, -1, 0, -21618, -1216265]	4	768
441.f3	441c4	[1, -1, 0, -17208, 867901]	2	768
441.f4	441c6	[1, -1, 0, -15003, -1979636]	2	1536
441.f5	441c2	[1, -1, 0, -1773, -5720]	4	384
441.f6	441c1	[1, -1, 0, 432, -869]	2	192	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 441.f have rank \(1\).

Modular form 441.2.a.f

Isogeny 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.