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

• Base field: \(\Q(\sqrt{35}) \)
• Label: 2.2.140.1-14.1-c
• 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-c over \(\Q(\sqrt{35}) \)

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

Curve label	Weierstrass Coefficients
14.1-c1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -8188 a - 48398\) , \( 966826 a + 5719868\bigr] \)
14.1-c2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -28 a - 118\) , \( -390 a - 2244\bigr] \)
14.1-c3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 212 a + 1302\) , \( 7434 a + 44044\bigr] \)
14.1-c4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1708 a - 10058\) , \( 72970 a + 431756\bigr] \)
14.1-c5	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -508 a - 2958\) , \( -16038 a - 94820\bigr] \)
14.1-c6	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -131068 a - 775438\) , \( 62562474 a + 370124604\bigr] \)

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