Elliptic curve isogeny class 36.1-f over number field 4.4.9792.1

• Base field: 4.4.9792.1
• Label: 4.4.9792.1-36.1-f
• Conductor: 36.1
• Rank: \( 0 \)

Base field 4.4.9792.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 2 x + 7 \); class number \(1\).

Elliptic curves in class 36.1-f over 4.4.9792.1

Isogeny class 36.1-f contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
36.1-f1	\( \bigl[a^{2} - 2 a - 4\) , \( -a^{3} + 3 a^{2} + 3 a - 3\) , \( -a^{3} + 4 a^{2} + 2 a - 7\) , \( -7 a^{3} + 19 a^{2} + 28 a - 22\) , \( -5 a^{3} + 12 a^{2} + 23 a - 9\bigr] \)
36.1-f2	\( \bigl[a^{2} - 2 a - 3\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 3\) , \( -16 a^{3} + a^{2} + 149 a + 150\) , \( 392 a^{3} - 414 a^{2} - 3077 a - 2425\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph