Elliptic curve isogeny class 1764.2-h over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1764.2-h
• Conductor: 1764.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1764.2-h over \(\Q(\sqrt{13}) \)

Isogeny class 1764.2-h contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
1764.2-h1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -171 a - 512\) , \( 3495 a + 2621\bigr] \)
1764.2-h2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -a - 2\) , \( -a - 1\bigr] \)
1764.2-h3	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 4 a + 13\) , \( 23 a + 17\bigr] \)
1764.2-h4	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -36 a - 107\) , \( 279 a + 209\bigr] \)
1764.2-h5	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -11 a - 32\) , \( -49 a - 37\bigr] \)
1764.2-h6	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -2731 a - 8192\) , \( 220583 a + 165437\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph