Elliptic curve isogeny class 10.3-a over number field \(\Q(\sqrt{161}) \)

• Base field: \(\Q(\sqrt{161}) \)
• Label: 2.2.161.1-10.3-a
• Conductor: 10.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 10.3-a over \(\Q(\sqrt{161}) \)

Isogeny class 10.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
10.3-a1	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -206 a - 1187\) , \( 3773 a + 22034\bigr] \)
10.3-a2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -3356 a - 19597\) , \( 249683 a + 1459204\bigr] \)
10.3-a3	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -3321 a - 19392\) , \( 255573 a + 1493626\bigr] \)
10.3-a4	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -53126 a - 310467\) , \( 16680403 a + 97485076\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph