Elliptic curve isogeny class 19.3-a over number field 4.4.17600.1

• Base field: 4.4.17600.1
• Label: 4.4.17600.1-19.3-a
• Conductor: 19.3
• 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 19.3-a over 4.4.17600.1

Isogeny class 19.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
19.3-a1	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{3} - 5 a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - 4 a - 3\) , \( -\frac{7}{2} a^{3} + 5 a^{2} + 28 a - 44\) , \( \frac{3}{2} a^{3} - 7 a^{2} - 20 a + 56\bigr] \)
19.3-a2	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 4 a + 3\) , \( \frac{1}{2} a^{2} + a - 4\) , \( 20 a^{3} - \frac{127}{2} a^{2} - 95 a + 307\) , \( \frac{1401}{2} a^{3} - 2130 a^{2} - 3336 a + 10146\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph