Elliptic curve isogeny class 225.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-225.1-b
• Conductor: 225.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 225.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 225.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
225.1-b1	\( \bigl[a\) , \( a\) , \( 1\) , \( -329 a - 657\) , \( -10557 a - 18475\bigr] \)
225.1-b2	\( \bigl[a\) , \( a\) , \( 1\) , \( a + 3\) , \( 3 a + 5\bigr] \)
225.1-b3	\( \bigl[a\) , \( a\) , \( 1\) , \( 106 a + 213\) , \( -333 a - 583\bigr] \)
225.1-b4	\( \bigl[a\) , \( a\) , \( 1\) , \( -29 a - 57\) , \( -117 a - 205\bigr] \)
225.1-b5	\( \bigl[a\) , \( a\) , \( 1\) , \( -14 a - 27\) , \( 27 a + 47\bigr] \)
225.1-b6	\( \bigl[a\) , \( a\) , \( 1\) , \( -404 a - 807\) , \( -7917 a - 13855\bigr] \)
225.1-b7	\( \bigl[a\) , \( a\) , \( 1\) , \( -239 a - 477\) , \( 2907 a + 5087\bigr] \)
225.1-b8	\( \bigl[a\) , \( a\) , \( 1\) , \( -6479 a - 12957\) , \( -474477 a - 830335\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph