Elliptic curve isogeny class 961.7-a over number field \(\Q(\zeta_{15})^+\)

• Base field: \(\Q(\zeta_{15})^+\)
• Label: 4.4.1125.1-961.7-a
• Conductor: 961.7
• 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 961.7-a over \(\Q(\zeta_{15})^+\)

Isogeny class 961.7-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
961.7-a1	\( \bigl[0\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -2 a^{3} - a^{2} + 7 a + 3\) , \( -7541548 a^{3} - 6237551 a^{2} + 18769617 a + 4127623\bigr] \)
961.7-a2	\( \bigl[0\) , \( a^{3} - 2 a + 1\) , \( a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 3 a\) , \( a^{3} + a^{2} - 2 a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph