Elliptic curve isogeny class 49.1-a over number field \(\Q(\zeta_{7})^+\)

• Base field: \(\Q(\zeta_{7})^+\)
• Label: 3.3.49.1-49.1-a
• Conductor: 49.1
• 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 49.1-a over \(\Q(\zeta_{7})^+\)

Isogeny class 49.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 62 a^{2} - 26 a - 156\) , \( -380 a^{2} + 192 a + 886\bigr] \)
49.1-a2	\( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a + 1\) , \( 2 a^{2} - a - 6\) , \( -9 a^{2} + 4 a + 20\bigr] \)
49.1-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
49.1-a4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph