Elliptic curve isogeny class 19.1-a over number field 4.4.5744.1

• Base field: 4.4.5744.1
• Label: 4.4.5744.1-19.1-a
• Conductor: 19.1
• Rank: \( 0 \)

Base field 4.4.5744.1

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

Elliptic curves in class 19.1-a over 4.4.5744.1

Isogeny class 19.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{3} - 4 a - 1\) , \( -2 a^{3} + a^{2} + 9 a + 1\) , \( a^{3} - 5 a - 1\) , \( 3 a^{3} - 7 a^{2} - 2 a + 6\) , \( 9 a^{3} - 19 a^{2} - 8 a + 6\bigr] \)
19.1-a2	\( \bigl[a^{2} - a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a + 1\) , \( -12 a^{3} + 11 a^{2} + 47 a - 15\) , \( 58 a^{3} - 42 a^{2} - 262 a + 77\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph