Elliptic curve isogeny class 75.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-75.1-b
• Conductor: 75.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 75.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 75.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
75.1-b1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 552 a - 1536\) , \( -20014 a + 55870\bigr] \)
75.1-b2	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 2 a + 4\) , \( 6 a - 10\bigr] \)
75.1-b3	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -173 a + 494\) , \( -1016 a + 2846\bigr] \)
75.1-b4	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 52 a - 136\) , \( -134 a + 380\bigr] \)
75.1-b5	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 27 a - 66\) , \( 104 a - 284\bigr] \)
75.1-b6	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 677 a - 1886\) , \( -14484 a + 40430\bigr] \)
75.1-b7	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 402 a - 1116\) , \( 6614 a - 18464\bigr] \)
75.1-b8	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 10802 a - 30236\) , \( -927354 a + 2588690\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph