Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{161}) \)

• Base field: \(\Q(\sqrt{161}) \)
• Label: 2.2.161.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{161}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 40 \); class number \(1\).

Elliptic curves in class 1.1-a over \(\Q(\sqrt{161}) \)

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 580 a - 3970\) , \( 23404 a - 160184\bigr] \)
1.1-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -580 a - 3390\) , \( -23404 a - 136780\bigr] \)
1.1-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 9860 a - 67485\) , \( 1339828 a - 9170170\bigr] \)
1.1-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -9860 a - 57625\) , \( -1339828 a - 7830342\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph