Elliptic curve isogeny class 36.1-g over number field 4.4.9792.1

• Base field: 4.4.9792.1
• Label: 4.4.9792.1-36.1-g
• Number of curves: 2
• Conductor: 36.1
• Rank: \( 1 \)

Base field 4.4.9792.1

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 36.1-g over 4.4.9792.1

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

Curve label	Weierstrass Coefficients
36.1-g1	\( \bigl[a\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 2 a^{3} - 8 a^{2} - a + 14\) , \( 12 a^{3} - 41 a^{2} - 24 a + 53\bigr] \)
36.1-g2	\( \bigl[a\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 102 a^{3} - 363 a^{2} - 161 a + 469\) , \( -1349 a^{3} + 4714 a^{2} + 2406 a - 6317\bigr] \)