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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.2-i
• 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-i over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.2-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
37632.2-i1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -64 a - 104\) , \( 492 a + 332\bigr] \)
37632.2-i2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -1164 a + 276\) , \( -14220 a + 11772\bigr] \)
37632.2-i3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 676 a - 124\) , \( 4116 a + 2940\bigr] \)
37632.2-i4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -84 a - 84\) , \( 324 a + 540\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph