Elliptic curve isogeny class 11.1-a over number field 4.4.11525.1

• Base field: 4.4.11525.1
• Label: 4.4.11525.1-11.1-a
• Conductor: 11.1
• Rank: \( 0 \)

Base field 4.4.11525.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 11 x^{2} + 5 x + 25 \); class number \(1\).

Elliptic curves in class 11.1-a over 4.4.11525.1

Isogeny class 11.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
11.1-a1	\( \bigl[a^{2} - a - 6\) , \( -\frac{1}{5} a^{3} - \frac{4}{5} a^{2} + \frac{6}{5} a + 6\) , \( a\) , \( -\frac{4}{5} a^{3} - \frac{21}{5} a^{2} + \frac{94}{5} a + 14\) , \( \frac{42}{5} a^{3} - \frac{182}{5} a^{2} - \frac{52}{5} a + 125\bigr] \)
11.1-a2	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( \frac{2}{5} a^{3} + \frac{13}{5} a^{2} - \frac{22}{5} a - 19\) , \( 2 a^{3} + 3 a^{2} - 18 a - 34\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph