Elliptic curve isogeny class 1225.2-c over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1225.2-c
• Conductor: 1225.2
• 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 1225.2-c over \(\Q(\sqrt{21}) \)

Isogeny class 1225.2-c contains 6 curves linked by isogenies of degrees dividing 147.

Curve label	Weierstrass Coefficients
1225.2-c1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -2439 a - 4448\) , \( -97582 a - 174547\bigr] \)
1225.2-c2	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 291 a - 1298\) , \( 7194 a - 16506\bigr] \)
1225.2-c3	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -919 a - 1848\) , \( -26136 a - 45656\bigr] \)
1225.2-c4	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 971 a - 2898\) , \( 27140 a - 74487\bigr] \)
1225.2-c5	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 2\) , \( -18 a + 48\bigr] \)
1225.2-c6	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a + 2\) , \( -1\bigr] \)