Elliptic curve isogeny class 15.1-a over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-15.1-a
• Conductor: 15.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 15.1-a over \(\Q(\sqrt{21}) \)

Isogeny class 15.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
15.1-a1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -a\) , \( -4 a - 7\bigr] \)
15.1-a2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 174 a + 260\) , \( 145 a + 374\bigr] \)
15.1-a3	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -41 a - 75\) , \( 73 a + 131\bigr] \)
15.1-a4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 27 a - 62\) , \( -106 a + 305\bigr] \)
15.1-a5	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 382 a - 1057\) , \( -6554 a + 18298\bigr] \)
15.1-a6	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 67 a - 177\) , \( 271 a - 757\bigr] \)

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