Elliptic curve isogeny class 1575.1-l over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1575.1-l
• Conductor: 1575.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1575.1-l over \(\Q(\sqrt{21}) \)

Isogeny class 1575.1-l contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1575.1-l1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 5632 a - 15788\) , \( 351477 a - 980809\bigr] \)
1575.1-l2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -53 a + 157\) , \( 441 a - 1213\bigr] \)
1575.1-l3	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 22 a - 68\) , \( 81 a - 223\bigr] \)
1575.1-l4	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 7 a - 23\) , \( -15 a + 41\bigr] \)
1575.1-l5	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 337 a - 1013\) , \( 5625 a - 15469\bigr] \)
1575.1-l6	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 82 a - 1358\) , \( 9549 a - 12013\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph