Elliptic curve isogeny class 25.1-b over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-25.1-b
• Conductor: 25.1
• Rank: \( 2 \)

Base field 4.4.8000.1

Generator \(a\), with minimal polynomial \( x^{4} - 10 x^{2} + 20 \); class number \(1\).

Elliptic curves in class 25.1-b over 4.4.8000.1

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

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( -4 a^{3} - 13 a^{2} + 8 a + 38\) , \( -19 a^{3} - \frac{105}{2} a^{2} + 51 a + 147\bigr] \)
25.1-b2	\( \bigl[a\) , \( \frac{1}{2} a^{2} + a - 2\) , \( a + 1\) , \( 8 a^{3} + 13 a^{2} - 56 a - 92\) , \( \frac{63}{2} a^{3} + \frac{105}{2} a^{2} - 227 a - 378\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph