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

• Base field: \(\Q(\sqrt{17}) \)
• Label: 2.2.17.1-900.1-i
• 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-i over \(\Q(\sqrt{17}) \)

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

Curve label	Weierstrass Coefficients
900.1-i1	\( \bigl[1\) , \( 0\) , \( 0\) , \( 157 a - 378\) , \( 1451 a - 3774\bigr] \)
900.1-i2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 7 a - 28\) , \( 21 a - 64\bigr] \)
900.1-i3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -135 a - 211\) , \( 1110 a + 1733\bigr] \)
900.1-i4	\( \bigl[1\) , \( 1\) , \( 1\) , \( 107 a - 275\) , \( 570 a - 1461\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph