Elliptic curve isogeny class 36.1-a over number field 4.4.10512.1

• Base field: 4.4.10512.1
• Label: 4.4.10512.1-36.1-a
• Conductor: 36.1
• Rank: \( 0 \)

Base field 4.4.10512.1

Generator \(a\), with minimal polynomial \( x^{4} - 7 x^{2} - 6 x + 1 \); class number \(1\).

Elliptic curves in class 36.1-a over 4.4.10512.1

Isogeny class 36.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
36.1-a1	\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{2} - 3\) , \( 853 a^{3} - 853 a^{2} - 4265 a - 2389\) , \( 2811 a^{3} - 20230 a^{2} + 16012 a + 57386\bigr] \)
36.1-a2	\( \bigl[a^{2} - a - 4\) , \( a\) , \( a^{2} - 3\) , \( 53 a^{3} - 53 a^{2} - 265 a - 149\) , \( 59 a^{3} - 294 a^{2} + 108 a + 714\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph