Elliptic curve isogeny class 25.3-c over number field 4.4.16357.1

• Base field: 4.4.16357.1
• Label: 4.4.16357.1-25.3-c
• Conductor: 25.3
• Rank: \( 0 \)

Base field 4.4.16357.1

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

Elliptic curves in class 25.3-c over 4.4.16357.1

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

Curve label	Weierstrass Coefficients
25.3-c1	\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 5 a + 5\) , \( a^{3} - 5 a\) , \( 11 a^{3} - 2 a^{2} - 72 a - 56\) , \( -47 a^{3} - 35 a^{2} + 263 a + 59\bigr] \)
25.3-c2	\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 5 a + 5\) , \( a^{3} - 5 a\) , \( -4 a^{3} - 7 a^{2} + 8 a + 9\) , \( -9 a^{3} - 19 a^{2} + 8 a + 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph