Elliptic curve isogeny class 900.1-k over number field \(\Q(\sqrt{17}) \)

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-900.1-k
• Conductor: 900.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 900.1-k over \(\Q(\sqrt{17}) \)

Isogeny class 900.1-k contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
900.1-k1	\( \bigl[1\) , \( 1\) , \( a\) , \( 630 a - 1900\) , \( 14271 a - 38564\bigr] \)
900.1-k2	\( \bigl[1\) , \( 1\) , \( a\) , \( 15 a - 25\) , \( 6 a - 23\bigr] \)
900.1-k3	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -163 a - 253\) , \( -812 a - 1268\bigr] \)
900.1-k4	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -11188 a - 17488\) , \( -926282 a - 1446470\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph