Elliptic curve isogeny class 21.4-a over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-21.4-a
• Conductor: 21.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 21.4-a over \(\Q(\sqrt{37}) \)

Isogeny class 21.4-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
21.4-a1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -5 a - 3\) , \( 109 a + 281\bigr] \)
21.4-a2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 11 a - 30\) , \( -24 a + 90\bigr] \)
21.4-a3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( a + 5\) , \( -a + 8\bigr] \)
21.4-a4	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -15 a - 28\) , \( 41 a + 109\bigr] \)

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