Elliptic curve isogeny class 71.1-a over number field 4.4.2225.1

• Base field: 4.4.2225.1
• Label: 4.4.2225.1-71.1-a
• Conductor: 71.1
• Rank: \( 0 \)

Base field 4.4.2225.1

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

Elliptic curves in class 71.1-a over 4.4.2225.1

Isogeny class 71.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
71.1-a1	\( \bigl[0\) , \( a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( -4 a^{3} - a^{2} + 10 a + 6\) , \( \frac{15}{2} a^{3} + \frac{13}{2} a^{2} - \frac{51}{2} a - 21\bigr] \)
71.1-a2	\( \bigl[0\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{27}{2} a^{3} + \frac{19}{2} a^{2} - \frac{143}{2} a - 78\) , \( 227 a^{3} - 273 a^{2} - 891 a + 503\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph