Elliptic curve isogeny class 36.1-a over number field 4.4.4752.1

• Base field: 4.4.4752.1
• Label: 4.4.4752.1-36.1-a
• Conductor: 36.1
• Rank: \( 0 \)

Base field 4.4.4752.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 3 x^{2} + 4 x + 1 \); class number \(1\).

Elliptic curves in class 36.1-a over 4.4.4752.1

Isogeny class 36.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
36.1-a1	\( \bigl[a^{3} - 4 a\) , \( a^{2} - a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 12 a^{3} - 36 a^{2} + 31 a - 8\) , \( -41 a^{3} + 168 a^{2} - 140 a - 5\bigr] \)
36.1-a2	\( \bigl[a^{3} - 4 a\) , \( 0\) , \( 0\) , \( -9 a^{3} - 6 a^{2} + 6 a + 3\) , \( -92 a^{3} - 52 a^{2} + 142 a + 32\bigr] \)
36.1-a3	\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( 5 a^{3} - 6 a^{2} - 18 a - 4\) , \( 23 a^{3} - 16 a^{2} - 98 a - 20\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph