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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.2-c
• Conductor: 37632.2
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
37632.2-c1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 64 a - 168\) , \( 492 a - 824\bigr] \)
37632.2-c2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1164 a - 888\) , \( -14220 a + 2448\bigr] \)
37632.2-c3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 84 a - 168\) , \( 324 a - 864\bigr] \)
37632.2-c4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -676 a + 552\) , \( 4116 a - 7056\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph