Elliptic curve isogeny class 1323.1-m over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1323.1-m
• Conductor: 1323.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1323.1-m over \(\Q(\sqrt{13}) \)

Isogeny class 1323.1-m contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1323.1-m1	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -34 a - 102\) , \( 868 a + 651\bigr] \)
1323.1-m2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( a + 3\) , \( 0\bigr] \)
1323.1-m3	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -4 a - 12\) , \( 4 a + 3\bigr] \)
1323.1-m4	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -39 a - 117\) , \( -360 a - 270\bigr] \)
1323.1-m5	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -49 a - 147\) , \( 544 a + 408\bigr] \)
1323.1-m6	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -784 a - 2352\) , \( 34060 a + 25545\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph