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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1875.1-bp
• Conductor: 1875.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
1875.1-bp1	\( \bigl[a\) , \( 0\) , \( 1\) , \( -9481 a - 17090\) , \( 787207 a + 1410516\bigr] \)
1875.1-bp2	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 17 a - 45\) , \( 456 a - 1278\bigr] \)
1875.1-bp3	\( \bigl[a\) , \( 0\) , \( 1\) , \( -1606 a - 2965\) , \( -39293 a - 70734\bigr] \)
1875.1-bp4	\( \bigl[a\) , \( 0\) , \( 1\) , \( -606 a - 1090\) , \( 11457 a + 20516\bigr] \)
1875.1-bp5	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 1017 a - 2920\) , \( -4419 a + 12722\bigr] \)
1875.1-bp6	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -4358 a + 10830\) , \( -35544 a + 119597\bigr] \)

Rank

Rank: \( 1 \)

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