Elliptic curve isogeny class 525.1-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-525.1-d
• Conductor: 525.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 525.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 525.1-d contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
525.1-d1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -32 a - 61\) , \( -224 a - 435\bigr] \)
525.1-d2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 3 a + 4\) , \( 2 a + 4\bigr] \)
525.1-d3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -2 a - 21\) , \( -30 a - 31\bigr] \)
525.1-d4	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -32 a - 96\) , \( 147 a + 209\bigr] \)
525.1-d5	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 33 a - 2611\) , \( -79 a - 53210\bigr] \)
525.1-d6	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -52 a - 346\) , \( -1475 a - 1111\bigr] \)
525.1-d7	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -512 a - 1086\) , \( -11511 a - 21445\bigr] \)
525.1-d8	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -8737 a - 15961\) , \( -697931 a - 1249420\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 6 & 12 & 4 & 12 & 2 & 4 \\ 3 & 1 & 2 & 4 & 12 & 4 & 6 & 12 \\ 6 & 2 & 1 & 2 & 6 & 2 & 3 & 6 \\ 12 & 4 & 2 & 1 & 3 & 4 & 6 & 12 \\ 4 & 12 & 6 & 3 & 1 & 12 & 2 & 4 \\ 12 & 4 & 2 & 4 & 12 & 1 & 6 & 3 \\ 2 & 6 & 3 & 6 & 2 & 6 & 1 & 2 \\ 4 & 12 & 6 & 12 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph