Elliptic curve isogeny class 1875.1-e over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1875.1-e
• Conductor: 1875.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1875.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 1875.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1875.1-e1	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 126 a - 2252\) , \( 2615 a - 41999\bigr] \)
1875.1-e2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( a - 2\) , \( -10 a + 1\bigr] \)
1875.1-e3	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 376 a - 1377\) , \( -7635 a + 22626\bigr] \)
1875.1-e4	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( a - 127\) , \( -260 a + 126\bigr] \)
1875.1-e5	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -374 a - 877\) , \( -7385 a - 13374\bigr] \)
1875.1-e6	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( -6874 a - 11502\) , \( -456885 a - 820249\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph