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

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

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

Curve label	Weierstrass Coefficients
1875.1-bj1	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -3 a\) , \( 9 a - 9\bigr] \)
1875.1-bj2	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 6872 a - 18375\) , \( 456884 a - 1277134\bigr] \)
1875.1-bj3	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 372 a - 1250\) , \( 7384 a - 20759\bigr] \)
1875.1-bj4	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -3 a - 125\) , \( 259 a - 134\bigr] \)
1875.1-bj5	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -128 a - 2125\) , \( -2616 a - 39384\bigr] \)
1875.1-bj6	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -378 a - 1000\) , \( 7634 a + 14991\bigr] \)

Rank

Rank: \( 0 \)

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