Elliptic curve isogeny class 128.2-c over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-128.2-c
• Conductor: 128.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 128.2-c over \(\Q(\sqrt{17}) \)

Isogeny class 128.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
128.2-c1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a - 23\) , \( 21 a - 54\bigr] \)
128.2-c2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 192 a - 491\) , \( -2076 a + 5318\bigr] \)
128.2-c3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 31\) , \( -32 a + 82\bigr] \)
128.2-c4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a - 19\) , \( -32 a - 50\bigr] \)
128.2-c5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a - 14\) , \( 21 a + 33\bigr] \)
128.2-c6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -192 a - 299\) , \( -2076 a - 3242\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph