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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1875.1-k
• 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-k over \(\Q(\sqrt{21}) \)

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

Curve label	Weierstrass Coefficients
1875.1-k1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -16 a - 28\) , \( -474 a - 849\bigr] \)
1875.1-k2	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4359 a + 6472\) , \( 39901 a + 90526\bigr] \)
1875.1-k3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -1016 a - 1903\) , \( 3401 a + 6401\bigr] \)
1875.1-k4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 605 a - 1696\) , \( -11457 a + 31973\bigr] \)
1875.1-k5	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 9480 a - 26571\) , \( -787207 a + 2197723\bigr] \)
1875.1-k6	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 1605 a - 4571\) , \( 39293 a - 110027\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph