Elliptic curve isogeny class 1089.1-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1089.1-d
• Conductor: 1089.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 1089.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 1089.1-d contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
1089.1-d1	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 23462 a - 70381\) , \( 3186418 a - 8768513\bigr] \)
1089.1-d2	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 32 a - 91\) , \( 268 a - 743\bigr] \)
1089.1-d3	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 2 a - 1\) , \( -2 a + 7\bigr] \)