Elliptic curve isogeny class 25.3-b over number field 4.4.8525.1

• Base field: 4.4.8525.1
• Label: 4.4.8525.1-25.3-b
• Conductor: 25.3
• Rank: \( 0 \)

Base field 4.4.8525.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 19 \); class number \(1\).

Elliptic curves in class 25.3-b over 4.4.8525.1

Isogeny class 25.3-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
25.3-b1	\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{2} - 4\) , \( 116 a^{3} + 46 a^{2} - 822 a - 923\) , \( -1369 a^{3} - 567 a^{2} + 9576 a + 10778\bigr] \)
25.3-b2	\( \bigl[a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{2} - 4\) , \( 11 a^{3} + 6 a^{2} - 77 a - 88\) , \( 5 a^{3} + 2 a^{2} - 33 a - 37\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph