Elliptic Curve Isogeny Class with LMFDB label 7605.g (Cremona label 7605q)

• Label: 7605.g
• Number of curves: 8
• Conductor: 7605
• CM: no
• Rank: 1

Elliptic curves in class 7605.g

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
7605.g1	7605q7	[1, -1, 1, -3285392, 2292896454]	[2]	73728
7605.g2	7605q5	[1, -1, 1, -205367, 35854134]	[2, 2]	36864
7605.g3	7605q8	[1, -1, 1, -167342, 49512714]	[2]	73728
7605.g4	7605q3	[1, -1, 1, -121712, -16313124]	[2]	18432
7605.g5	7605q4	[1, -1, 1, -15242, 338784]	[2, 2]	18432
7605.g6	7605q2	[1, -1, 1, -7637, -251364]	[2, 2]	9216
7605.g7	7605q1	[1, -1, 1, -32, -11046]	[2]	4608	\(\Gamma_0(N)\)-optimal
7605.g8	7605q6	[1, -1, 1, 53203, 2501646]	[2]	36864

Rank

The elliptic curves in class 7605.g have rank \(1\).

Modular form 7605.2.a.g

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.