Elliptic curve isogeny class 11.1-a over number field 4.4.14272.1

• Base field: 4.4.14272.1
• Label: 4.4.14272.1-11.1-a
• Conductor: 11.1
• Rank: \( 1 \)

Base field 4.4.14272.1

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

Elliptic curves in class 11.1-a over 4.4.14272.1

Isogeny class 11.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
11.1-a1	\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 1\) , \( -2 a^{2} - a\) , \( -a^{2} - a\bigr] \)
11.1-a2	\( \bigl[2 a^{3} - 5 a^{2} - 5 a + 5\) , \( a^{3} - 3 a^{2} - 2 a + 2\) , \( a^{3} - 3 a^{2} - 2 a + 3\) , \( 4 a^{3} - 12 a^{2} - 7 a + 20\) , \( 10 a^{3} - 19 a^{2} - 44 a + 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph