Elliptic curve isogeny class 113.2-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-113.2-a
• Conductor: 113.2
• Rank: \( 0 \)

Base field \(\Q(\zeta_{7})^+\)

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

Elliptic curves in class 113.2-a over \(\Q(\zeta_{7})^+\)

Isogeny class 113.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
113.2-a1	\( \bigl[a + 1\) , \( a^{2} + a - 3\) , \( a^{2} - 1\) , \( -75 a^{2} + 175 a - 73\) , \( -547 a^{2} + 1231 a - 448\bigr] \)
113.2-a2	\( \bigl[a + 1\) , \( a^{2} + a - 3\) , \( a^{2} - 1\) , \( -15 a^{2} + 5 a - 13\) , \( -55 a^{2} - 69 a + 74\bigr] \)
113.2-a3	\( \bigl[a + 1\) , \( a^{2} + a - 3\) , \( a^{2} - 1\) , \( -5 a^{2} + 10 a - 3\) , \( -7 a^{2} + 11 a - 3\bigr] \)
113.2-a4	\( \bigl[a + 1\) , \( a^{2} + a - 3\) , \( a^{2} - 1\) , \( 2\) , \( a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph