Elliptic curve isogeny class 175.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-175.1-b
• Conductor: 175.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 175.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 175.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
175.1-b1	\( \bigl[0\) , \( a\) , \( 1\) , \( 657 a - 1837\) , \( -14938 a + 41697\bigr] \)
175.1-b2	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -7 a - 10\) , \( -12 a - 21\bigr] \)
175.1-b3	\( \bigl[0\) , \( a\) , \( 1\) , \( -43 a + 123\) , \( -14 a + 40\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph