Elliptic curve isogeny class 1089.2-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1089.2-a
• Conductor: 1089.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 1089.2-a over \(\Q(\sqrt{13}) \)

Isogeny class 1089.2-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
1089.2-a1	\( \bigl[0\) , \( a\) , \( 1\) , \( -7820 a - 23460\) , \( 1054319 a + 790739\bigr] \)
1089.2-a2	\( \bigl[0\) , \( a\) , \( 1\) , \( -10 a - 30\) , \( 79 a + 59\bigr] \)
1089.2-a3	\( \bigl[0\) , \( a\) , \( 1\) , \( 0\) , \( -a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph