Elliptic curve isogeny class 256.1-c over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-256.1-c
• Conductor: 256.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 256.1-c over \(\Q(\sqrt{17}) \)

Isogeny class 256.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
256.1-c1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -267 a - 420\) , \( 7254 a + 11336\bigr] \)
256.1-c2	\( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 2\) , \( a - 1\bigr] \)
256.1-c3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -27 a - 40\) , \( 26 a + 40\bigr] \)
256.1-c4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a\) , \( -a\bigr] \)
256.1-c5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 347 a - 887\) , \( -4862 a + 12454\bigr] \)
256.1-c6	\( \bigl[0\) , \( -a\) , \( 0\) , \( 267 a - 687\) , \( -7254 a + 18590\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph