Elliptic curve isogeny class 9.1-b over number field \(\Q(\sqrt{97}) \)

• Base field: \(\Q(\sqrt{97}) \)
• Label: 2.2.97.1-9.1-b
• Conductor: 9.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{97}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 24 \); class number \(1\).

Elliptic curves in class 9.1-b over \(\Q(\sqrt{97}) \)

Isogeny class 9.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
9.1-b1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -171898 a + 932448\) , \( -41983520 a + 227736619\bigr] \)
9.1-b2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 171898 a + 760550\) , \( 41983520 a + 185753099\bigr] \)
9.1-b3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -48292 a - 213665\) , \( 5535380 a + 24490895\bigr] \)
9.1-b4	\( \bigl[1\) , \( 0\) , \( 1\) , \( 48292 a - 261957\) , \( -5535380 a + 30026275\bigr] \)
9.1-b5	\( \bigl[1\) , \( 0\) , \( 1\) , \( 804 a - 4362\) , \( 27606 a - 149747\bigr] \)
9.1-b6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -804 a - 3558\) , \( -27606 a - 122141\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph