Elliptic curve isogeny class 25.1-c over number field 4.4.16997.1

• Base field: 4.4.16997.1
• Label: 4.4.16997.1-25.1-c
• Conductor: 25.1
• Rank: \( 1 \)

Base field 4.4.16997.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - x + 5 \); class number \(1\).

Elliptic curves in class 25.1-c over 4.4.16997.1

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

Curve label	Weierstrass Coefficients
25.1-c1	\( \bigl[a^{2} + a - 3\) , \( -a^{3} + 3 a + 1\) , \( a^{2} + a - 3\) , \( 90 a^{3} + 216 a^{2} - 38 a - 197\) , \( -92 a^{3} - 215 a^{2} + 46 a + 194\bigr] \)
25.1-c2	\( \bigl[a^{2} + a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 6\) , \( a\) , \( 3 a^{3} - 2 a^{2} - 12 a + 10\) , \( 6 a^{3} - 8 a^{2} - 16 a + 15\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph