Elliptic curve isogeny class 36.1-h over number field 4.4.9792.1

• Base field: 4.4.9792.1
• Label: 4.4.9792.1-36.1-h
• 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-h over 4.4.9792.1

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

Curve label	Weierstrass Coefficients
36.1-h1	\( \bigl[1\) , \( -a^{3} + 3 a^{2} + 2 a - 5\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( -6184 a^{3} + 21515 a^{2} + 11467 a - 29331\) , \( -856340 a^{3} + 2982695 a^{2} + 1570802 a - 4042118\bigr] \)
36.1-h2	\( \bigl[a^{3} - 3 a^{2} - 2 a + 4\) , \( -2 a^{3} + 7 a^{2} + 5 a - 13\) , \( a\) , \( -6 a^{3} + 20 a^{2} + 18 a - 35\) , \( -6 a^{3} + 20 a^{2} + 18 a - 36\bigr] \)