Elliptic curve isogeny class 324.5-c over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-324.5-c
• Conductor: 324.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 324.5-c over \(\Q(\sqrt{37}) \)

Isogeny class 324.5-c contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
324.5-c1	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -9 a - 19\) , \( 18 a + 45\bigr] \)
324.5-c2	\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 15 a - 55\) , \( -57 a + 202\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph