Elliptic curve isogeny class 1575.1-p over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1575.1-p
• Conductor: 1575.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1575.1-p over \(\Q(\sqrt{21}) \)

Isogeny class 1575.1-p contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
1575.1-p1	\( \bigl[a\) , \( -1\) , \( 1\) , \( -83 a - 1275\) , \( -9549 a - 2464\bigr] \)
1575.1-p2	\( \bigl[a\) , \( -1\) , \( 1\) , \( 52 a + 105\) , \( -441 a - 772\bigr] \)
1575.1-p3	\( \bigl[a\) , \( -1\) , \( 1\) , \( -23 a - 45\) , \( -81 a - 142\bigr] \)
1575.1-p4	\( \bigl[a\) , \( -1\) , \( 1\) , \( -8 a - 15\) , \( 15 a + 26\bigr] \)
1575.1-p5	\( \bigl[a\) , \( -1\) , \( 1\) , \( -338 a - 675\) , \( -5625 a - 9844\bigr] \)
1575.1-p6	\( \bigl[a\) , \( -1\) , \( 1\) , \( -5633 a - 10155\) , \( -351477 a - 629332\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph