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

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

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

Curve label	Weierstrass Coefficients
1089.1-c1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -2 a + 5\) , \( 6 a - 16\bigr] \)
1089.1-c2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -97 a - 137\) , \( 141 a + 174\bigr] \)
1089.1-c3	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 23 a - 55\) , \( 67 a - 157\bigr] \)
1089.1-c4	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 78 a - 220\) , \( -549 a + 1328\bigr] \)

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