Elliptic curve isogeny class 25.1-a over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-25.1-a
• Conductor: 25.1
• Rank: \( 0 \)

Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 25.1-a over 4.4.19821.1

Isogeny class 25.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( a + 1\) , \( 3 a^{3} + a^{2} - 30 a + 3\) , \( -\frac{22}{3} a^{3} - \frac{1}{3} a^{2} + 53 a + 26\bigr] \)
25.1-a2	\( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 1\) , \( a + 1\) , \( \frac{14}{3} a^{3} - \frac{22}{3} a^{2} - 20 a + 3\) , \( -\frac{37}{3} a^{3} + \frac{32}{3} a^{2} + 67 a + 16\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph