Elliptic curve isogeny class 36.2-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-36.2-a
• Conductor: 36.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 36.2-a over \(\Q(\sqrt{13}) \)

Isogeny class 36.2-a contains 6 curves linked by isogenies of degrees dividing 45.

Curve label	Weierstrass Coefficients
36.2-a1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -113 a - 80\) , \( 590 a + 599\bigr] \)
36.2-a2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 3 a - 8\) , \( 14 a - 35\bigr] \)
36.2-a3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 124 a - 297\) , \( 1087 a - 2492\bigr] \)
36.2-a4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2 a - 5\) , \( -5 a + 11\bigr] \)
36.2-a5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -a + 3\) , \( -3 a + 7\bigr] \)
36.2-a6	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 87 a + 6\) , \( 358 a + 111\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 45 & 3 & 5 & 15 & 9 \\ 45 & 1 & 15 & 9 & 3 & 5 \\ 3 & 15 & 1 & 15 & 5 & 3 \\ 5 & 9 & 15 & 1 & 3 & 45 \\ 15 & 3 & 5 & 3 & 1 & 15 \\ 9 & 5 & 3 & 45 & 15 & 1 \end{array}\right)\)

Isogeny graph