Elliptic curve isogeny class 14.1-d over number field \(\Q(\sqrt{35}) \)

• Base field: \(\Q(\sqrt{35}) \)
• Label: 2.2.140.1-14.1-d
• Conductor: 14.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{35}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 35 \); class number \(2\).

Elliptic curves in class 14.1-d over \(\Q(\sqrt{35}) \)

Isogeny class 14.1-d contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
14.1-d1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -8182 a - 48398\) , \( -1015936 a - 6010364\bigr] \)
14.1-d2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -22 a - 118\) , \( 240 a + 1428\bigr] \)
14.1-d3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 218 a + 1302\) , \( -6144 a - 36340\bigr] \)
14.1-d4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -1702 a - 10058\) , \( -83200 a - 492212\bigr] \)
14.1-d5	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -502 a - 2958\) , \( 13008 a + 76964\bigr] \)
14.1-d6	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -131062 a - 775438\) , \( -63348864 a - 374777340\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph