Elliptic curve isogeny class 961.9-a over number field \(\Q(\zeta_{15})^+\)

• Base field: \(\Q(\zeta_{15})^+\)
• Label: 4.4.1125.1-961.9-a
• Conductor: 961.9
• Rank: \( 1 \)

Base field \(\Q(\zeta_{15})^+\)

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

Elliptic curves in class 961.9-a over \(\Q(\zeta_{15})^+\)

Isogeny class 961.9-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
961.9-a1	\( \bigl[0\) , \( -a^{3} + 2 a - 1\) , \( a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a\) , \( -a^{2} - a + 3\bigr] \)
961.9-a2	\( \bigl[0\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -2 a^{3} - a^{2} + 7 a + 3\) , \( -6908 a^{3} - 5713 a^{2} + 17194 a + 3781\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph