Elliptic curve isogeny class 113.3-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-113.3-a
• Conductor: 113.3
• 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 113.3-a over \(\Q(\zeta_{7})^+\)

Isogeny class 113.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
113.3-a1	\( \bigl[a^{2} - 1\) , \( a + 1\) , \( 0\) , \( 11 a^{2} - 14 a - 50\) , \( 80 a^{2} - 60 a - 175\bigr] \)
113.3-a2	\( \bigl[a^{2} - 1\) , \( a + 1\) , \( 0\) , \( -4 a^{2} - 4 a\) , \( -18 a^{2} - 17 a + 7\bigr] \)
113.3-a3	\( \bigl[a^{2} - 1\) , \( a + 1\) , \( 0\) , \( a^{2} + a\) , \( 0\bigr] \)
113.3-a4	\( \bigl[a^{2} - 1\) , \( a + 1\) , \( 0\) , \( -99 a^{2} - 74 a + 50\) , \( -908 a^{2} - 722 a + 497\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph