Elliptic curve isogeny class 100.1-a over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-100.1-a
• Conductor: 100.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 100.1-a over \(\Q(\sqrt{13}) \)

Isogeny class 100.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
100.1-a1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 17 a - 35\) , \( -12 a + 29\bigr] \)
100.1-a2	\( \bigl[1\) , \( 1\) , \( a\) , \( -6 a - 123\) , \( 297 a - 145\bigr] \)
100.1-a3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 137 a - 315\) , \( 1204 a - 2779\bigr] \)
100.1-a4	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 35 a - 89\) , \( -156 a + 346\bigr] \)
100.1-a5	\( \bigl[1\) , \( 1\) , \( a\) , \( -36 a - 53\) , \( 155 a + 191\bigr] \)
100.1-a6	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 5 a - 129\) , \( -298 a + 152\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph