Elliptic curve isogeny class 21.1-a over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-21.1-a
• Conductor: 21.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{37}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 9 \); class number \(1\).

Elliptic curves in class 21.1-a over \(\Q(\sqrt{37}) \)

Isogeny class 21.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
21.1-a1	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 14 a - 43\) , \( -41 a + 150\bigr] \)
21.1-a2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -a + 6\) , \( a + 7\bigr] \)
21.1-a3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -11 a - 19\) , \( 24 a + 66\bigr] \)
21.1-a4	\( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 4 a - 8\) , \( -109 a + 390\bigr] \)

Rank

Rank: \( 1 \)

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