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

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1089.1-e
• Conductor: 1089.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
1089.1-e1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( a + 4\) , \( -7 a - 9\bigr] \)
1089.1-e2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -79 a - 141\) , \( 548 a + 780\bigr] \)
1089.1-e3	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -24 a - 31\) , \( -68 a - 89\bigr] \)
1089.1-e4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 99 a - 238\) , \( -379 a + 849\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph