Elliptic curve isogeny class 10.2-g over number field \(\Q(\sqrt{161}) \)

• Base field: \(\Q(\sqrt{161}) \)
• Label: 2.2.161.1-10.2-g
• Conductor: 10.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 10.2-g over \(\Q(\sqrt{161}) \)

Isogeny class 10.2-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
10.2-g1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 282395 a + 1650409\) , \( 167656296 a + 979831807\bigr] \)
10.2-g2	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -1486970 a - 8690271\) , \( 1534139743 a + 8965955671\bigr] \)
10.2-g3	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -10132525 a - 59217391\) , \( -43084599702 a - 251798842209\bigr] \)
10.2-g4	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -21151255 a - 123614031\) , \( 133392826696 a + 779586199087\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph