Elliptic curve isogeny class 4.1-a over number field 4.4.13968.1

• Base field: 4.4.13968.1
• Label: 4.4.13968.1-4.1-a
• Conductor: 4.1
• Rank: \( 1 \)

Base field 4.4.13968.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 4 \); class number \(1\).

Elliptic curves in class 4.1-a over 4.4.13968.1

Isogeny class 4.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[0\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a - 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( a^{2} - 2 a + 1\) , \( -7 a^{3} + \frac{9}{2} a^{2} + \frac{103}{2} a + 18\bigr] \)
4.1-a2	\( \bigl[0\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( a^{2} - 2 a + 1\) , \( \frac{13}{2} a^{3} - \frac{11}{2} a^{2} - 51 a - 18\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph