Elliptic curve isogeny class 181.1-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-181.1-a
• Conductor: 181.1
• 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 181.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 181.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
181.1-a1	\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( a^{2} + a - 2\) , \( -103 a^{2} + 277 a - 152\) , \( -1191 a^{2} + 2790 a - 1144\bigr] \)
181.1-a2	\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( a^{2} + a - 2\) , \( 2 a^{2} + 2 a - 2\) , \( a^{2} + 2 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph