Elliptic Curve Isogeny Class 42.a (Cremona label 42a)

• Label: 42.a
• Number of curves: 6
• Conductor: \(42\)
• CM: no
• Rank: \(0\)

Elliptic curves in class 42.a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion order	Modular degree	Optimality
42.a1	42a4	[1, 1, 1, -1344, 18405]	4	16
42.a2	42a5	[1, 1, 1, -914, -10915]	2	32
42.a3	42a3	[1, 1, 1, -104, 101]	4	16
42.a4	42a2	[1, 1, 1, -84, 261]	8	8
42.a5	42a1	[1, 1, 1, -4, 5]	8	4	\(\Gamma_0(N)\)-optimal
42.a6	42a6	[1, 1, 1, 386, 1277]	2	32

Rank

The elliptic curves in class 42.a have rank \(0\).

Modular form 42.2.1.a

Isogeny matrix

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

Isogeny graph