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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-900.1-l
• Conductor: 900.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
900.1-l1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 307 a - 793\) , \( -3967 a + 10155\bigr] \)
900.1-l2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 79177 a - 202913\) , \( -17346237 a + 44433043\bigr] \)
900.1-l3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 4927 a - 12713\) , \( -267627 a + 685243\bigr] \)
900.1-l4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 4597 a - 13233\) , \( -272457 a + 677155\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph