Elliptic curve isogeny class 108.2-c over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-108.2-c
• Conductor: 108.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 108.2-c over \(\Q(\sqrt{13}) \)

Isogeny class 108.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
108.2-c1	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -16 a + 40\) , \( 0\bigr] \)
108.2-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( a - 1\) , \( -3 a - 5\bigr] \)
108.2-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -9 a - 51\) , \( -41 a - 141\bigr] \)
108.2-c4	\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 64 a - 160\) , \( -16 a - 8\bigr] \)