Elliptic curve isogeny class 25.1-b over number field 4.4.11661.1

• Base field: 4.4.11661.1
• Label: 4.4.11661.1-25.1-b
• Conductor: 25.1
• Rank: \( 1 \)

Base field 4.4.11661.1

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

Elliptic curves in class 25.1-b over 4.4.11661.1

Isogeny class 25.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[a^{3} - 4 a - 2\) , \( -a^{3} + 4 a + 3\) , \( a^{3} - 5 a - 1\) , \( -4 a^{3} + 18 a + 16\) , \( -7 a^{3} + 4 a^{2} + 32 a + 12\bigr] \)
25.1-b2	\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( a\) , \( -571 a^{3} + 1394 a^{2} + 1664 a - 3626\) , \( -14067 a^{3} + 34739 a^{2} + 40001 a - 89335\bigr] \)
25.1-b3	\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( a\) , \( -11 a^{3} + 19 a^{2} + 39 a - 36\) , \( -23 a^{3} + 50 a^{2} + 72 a - 118\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph