Elliptic curve isogeny class 1225.3-c over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1225.3-c
• Conductor: 1225.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 147 & 3 & 49 & 7 & 21 \\ 147 & 1 & 49 & 3 & 21 & 7 \\ 3 & 49 & 1 & 147 & 21 & 7 \\ 49 & 3 & 147 & 1 & 7 & 21 \\ 7 & 21 & 21 & 7 & 1 & 3 \\ 21 & 7 & 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 1225.3-c over \(\Q(\sqrt{21}) \)

Isogeny class 1225.3-c contains 6 curves linked by isogenies of degrees dividing 147.

Curve label	Weierstrass Coefficients
1225.3-c1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 921 a - 2768\) , \( 25216 a - 69024\bigr] \)
1225.3-c2	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -969 a - 1928\) , \( -28110 a - 49275\bigr] \)
1225.3-c3	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 2441 a - 6888\) , \( 100022 a - 279017\bigr] \)
1225.3-c4	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -289 a - 1008\) , \( -6904 a - 8304\bigr] \)
1225.3-c5	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 2\) , \( -3\bigr] \)
1225.3-c6	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( 18 a + 32\bigr] \)