Elliptic curve isogeny class 1.1-a over number field 4.4.13768.1

• Base field: 4.4.13768.1
• Label: 4.4.13768.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

Base field 4.4.13768.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 5 x^{2} + 2 x + 2 \); class number \(1\).

Elliptic curves in class 1.1-a over 4.4.13768.1

Isogeny class 1.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[a^{3} - 5 a - 2\) , \( -a^{3} + 4 a + 1\) , \( a^{2} - 3\) , \( -9 a^{3} + 5 a^{2} + 45 a + 3\) , \( -14 a^{3} + 8 a^{2} + 67 a + 4\bigr] \)
1.1-a2	\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a + 1\) , \( -a^{3} + 5 a + 5\) , \( a^{2} + 2 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph