Elliptic curve isogeny class 324.1-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-324.1-a
• Conductor: 324.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 324.1-a over \(\Q(\sqrt{13}) \)

Isogeny class 324.1-a contains 6 curves linked by isogenies of degrees dividing 45.

Curve label	Weierstrass Coefficients
324.1-a1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -257 a + 13\) , \( 1140 a + 2856\bigr] \)
324.1-a2	\( \bigl[1\) , \( -1\) , \( a\) , \( -14 a - 18\) , \( -34 a - 44\bigr] \)
324.1-a3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 669 a - 1560\) , \( -13229 a + 30488\bigr] \)
324.1-a4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 13 a - 32\) , \( 33 a - 78\bigr] \)
324.1-a5	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -6 a + 15\) , \( 37 a - 85\bigr] \)
324.1-a6	\( \bigl[1\) , \( -1\) , \( a\) , \( 256 a - 243\) , \( -1141 a + 3997\bigr] \)

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