Elliptic curve isogeny class 108.1-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-108.1-b
• Conductor: 108.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 108.1-b over \(\Q(\sqrt{13}) \)

Isogeny class 108.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
108.1-b1	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a + 1\) , \( a - 5\bigr] \)
108.1-b2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 90 a + 117\) , \( 117 a + 152\bigr] \)
108.1-b3	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -350 a - 483\) , \( -499 a - 688\bigr] \)
108.1-b4	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 9 a - 29\) , \( 21 a - 47\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph