Elliptic curve isogeny class 36.1-e over number field 4.4.9792.1

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

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

Curve label	Weierstrass Coefficients
36.1-e1	\( \bigl[a^{2} - a - 4\) , \( -2 a^{3} + 7 a^{2} + 4 a - 11\) , \( 1\) , \( -18 a^{3} + 27 a^{2} - 358 a - 617\) , \( 71 a^{3} + 1113 a^{2} + 4748 a + 4759\bigr] \)
36.1-e2	\( \bigl[a^{2} - a - 4\) , \( -2 a^{3} + 7 a^{2} + 4 a - 11\) , \( 1\) , \( 2 a^{3} - 8 a^{2} - 3 a + 13\) , \( 11 a^{3} - 46 a^{2} - 21 a + 62\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph