Elliptic Curve Isogeny Class 4.1-b over Number Field \(\Q(\sqrt{89}) \)

• Base field: \(\Q(\sqrt{89}) \)
• Label: 2.2.89.1-4.1-b
• Conductor: 4.1
• Rank: not recorded

Base field \(\Q(\sqrt{89}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 22 \); class number \(1\).

Elliptic curves in class 4.1-b over \(\Q(\sqrt{89}) \)

Isogeny class 4.1-b contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
4.1-b1	\( \bigl[1\) , \( -1\) , \( 0\) , \( 5 a - 28\) , \( 13 a - 66\bigr] \)
4.1-b2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 72875 a - 380188\) , \( -20764677 a + 108329124\bigr] \)
4.1-b3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -4715 a - 19883\) , \( 177745 a + 749549\bigr] \)
4.1-b4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -72875 a - 307313\) , \( 20764677 a + 87564447\bigr] \)
4.1-b5	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2365 a - 9973\) , \( -133485 a - 562905\bigr] \)
4.1-b6	\( \bigl[1\) , \( -1\) , \( 0\) , \( 2365 a - 12338\) , \( 133485 a - 696390\bigr] \)
4.1-b7	\( \bigl[1\) , \( -1\) , \( 0\) , \( -5 a - 23\) , \( -13 a - 53\bigr] \)
4.1-b8	\( \bigl[1\) , \( -1\) , \( 0\) , \( 4715 a - 24598\) , \( -177745 a + 927294\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 20 & 4 & 10 & 2 & 20 & 4 \\ 5 & 1 & 4 & 20 & 2 & 10 & 4 & 20 \\ 20 & 4 & 1 & 20 & 2 & 10 & 4 & 5 \\ 4 & 20 & 20 & 1 & 10 & 2 & 5 & 4 \\ 10 & 2 & 2 & 10 & 1 & 5 & 2 & 10 \\ 2 & 10 & 10 & 2 & 5 & 1 & 10 & 2 \\ 20 & 4 & 4 & 5 & 2 & 10 & 1 & 20 \\ 4 & 20 & 5 & 4 & 10 & 2 & 20 & 1 \end{array}\right)\)

Isogeny graph