Elliptic curve isogeny class 324.1-w over number field \(\Q(\sqrt{37}) \)

• Base field: \(\Q(\sqrt{37}) \)
• Label: 2.2.37.1-324.1-w
• Conductor: 324.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 324.1-w over \(\Q(\sqrt{37}) \)

Isogeny class 324.1-w contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
324.1-w1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -11808 a - 30110\) , \( 1223438 a + 3110037\bigr] \)
324.1-w2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -18 a - 50\) , \( 86 a + 213\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph