Elliptic curve isogeny class 19.2-a over number field 4.4.17600.1

• Base field: 4.4.17600.1
• Label: 4.4.17600.1-19.2-a
• Conductor: 19.2
• Rank: \( 0 \)

Base field 4.4.17600.1

Generator \(a\), with minimal polynomial \( x^{4} - 14 x^{2} + 44 \); class number \(1\).

Elliptic curves in class 19.2-a over 4.4.17600.1

Isogeny class 19.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
19.2-a1	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} + 5 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 3\) , \( 3 a^{3} + 5 a^{2} - 26 a - 44\) , \( -\frac{3}{2} a^{3} - 7 a^{2} + 19 a + 56\bigr] \)
19.2-a2	\( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 4\) , \( \frac{1}{2} a^{2} + a - 4\) , \( -\frac{9}{2} a^{3} - 6 a^{2} + 26 a + 19\) , \( -33 a^{3} - 102 a^{2} + 153 a + 490\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph