Elliptic Curve Isogeny Class 27.1-a over Number Field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-27.1-a
• Conductor: 27.1
• Rank: not recorded

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

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

Elliptic curves in class 27.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 27.1-a contains 2 curves linked by isogenies of degree 13.

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[0\) , \( -a\) , \( a\) , \( 652 a^{2} - 391 a - 1564\) , \( 10528 a^{2} - 5979 a - 24046\bigr] \)
27.1-a2	\( \bigl[0\) , \( -a\) , \( a\) , \( 2 a^{2} - a - 4\) , \( -2 a^{2} + a + 4\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph