Elliptic curve isogeny class 1089.1-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1089.1-b
• Conductor: 1089.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1089.1-b over \(\Q(\sqrt{13}) \)

Isogeny class 1089.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1089.1-b1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -2 a - 1\) , \( -1\bigr] \)
1089.1-b2	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( -17 a - 31\) , \( 45 a + 53\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph