Elliptic curve isogeny class 1452.1-h over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1452.1-h
• Conductor: 1452.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1452.1-h over \(\Q(\sqrt{21}) \)

Isogeny class 1452.1-h contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
1452.1-h1	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 202 a - 568\) , \( -13136 a + 36667\bigr] \)
1452.1-h2	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -23 a + 62\) , \( 463 a - 1295\bigr] \)
1452.1-h3	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 27 a - 78\) , \( 129 a - 363\bigr] \)
1452.1-h4	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 402 a - 1128\) , \( -6408 a + 17883\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph