Elliptic curve isogeny class 9.1-a over number field 4.4.19225.1

• Base field: 4.4.19225.1
• Label: 4.4.19225.1-9.1-a
• Conductor: 9.1
• Rank: \( 1 \)

Base field 4.4.19225.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 15 x^{2} + 2 x + 44 \); class number \(1\).

Elliptic curves in class 9.1-a over 4.4.19225.1

Isogeny class 9.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
9.1-a1	\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 14\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{5}{2} a - 7\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 15\) , \( -\frac{5}{2} a^{3} + \frac{21}{2} a^{2} + \frac{19}{2} a - 66\) , \( -a^{3} + 11 a^{2} - 8 a - 94\bigr] \)
9.1-a2	\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{7}{2} a + 8\) , \( a^{3} - 4 a^{2} - 5 a + 23\) , \( 0\) , \( \frac{3649}{2} a^{3} - \frac{12823}{2} a^{2} - \frac{22507}{2} a + 31952\) , \( \frac{127687}{2} a^{3} - \frac{448621}{2} a^{2} - \frac{787731}{2} a + 1117652\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph