Elliptic curve isogeny class 37632.2-j over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.2-j
• Conductor: 37632.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-3}) \)

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

Elliptic curves in class 37632.2-j over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.2-j contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
37632.2-j1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 299 a + 122\) , \( -1431 a + 3309\bigr] \)
37632.2-j2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 19 a - 18\) , \( -115 a + 145\bigr] \)
37632.2-j3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -66 a + 37\) , \( 91 a - 182\bigr] \)
37632.2-j4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -21 a + 7\) , \( -26 a + 22\bigr] \)
37632.2-j5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 379 a - 558\) , \( -4255 a + 4213\bigr] \)
37632.2-j6	\( \bigl[0\) , \( -a\) , \( 0\) , \( -336 a + 112\) , \( -1916 a + 1828\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 2 & 8 & 4 \\ 4 & 2 & 2 & 1 & 4 & 2 \\ 4 & 2 & 8 & 4 & 1 & 8 \\ 8 & 4 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph