Elliptic curve isogeny class 19.1-a over number field 4.4.19429.1

• Base field: 4.4.19429.1
• Label: 4.4.19429.1-19.1-a
• Conductor: 19.1
• Rank: \( 1 \)

Base field 4.4.19429.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} - x + 5 \); class number \(1\).

Elliptic curves in class 19.1-a over 4.4.19429.1

Isogeny class 19.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
19.1-a1	\( \bigl[a^{3} - a^{2} - 5 a - 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{2} - 3\) , \( 5 a^{3} - 19 a^{2} - 50 a - 3\) , \( -12 a^{3} - 83 a^{2} - 130 a - 38\bigr] \)
19.1-a2	\( \bigl[a^{3} - a^{2} - 5 a - 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph