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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1089.1-d
• 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-d over \(\Q(\sqrt{13}) \)

Isogeny class 1089.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1089.1-d1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \)
1089.1-d2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \)
1089.1-d3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -6\) , \( -9\bigr] \)
1089.1-d4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)

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