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

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

Isogeny class 181.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
181.1-b1	\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a\) , \( -44 a^{2} - 51 a - 3\) , \( -269 a^{2} - 293 a + 65\bigr] \)
181.1-b2	\( \bigl[a^{2} - 2\) , \( -a^{2} + 2\) , \( a\) , \( -4 a^{2} + 4 a + 2\) , \( a^{2} - 4 a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph