Elliptic curve isogeny class 69312.1-f over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-69312.1-f
• Conductor: 69312.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 69312.1-f over \(\Q(\sqrt{-3}) \)

Isogeny class 69312.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
69312.1-f1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4674 a - 3405\) , \( 112431 a - 14757\bigr] \)
69312.1-f2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 914 a - 3885\) , \( -29985 a + 90939\bigr] \)
69312.1-f3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 234 a - 285\) , \( 1575 a + 1323\bigr] \)
69312.1-f4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -86 a + 135\) , \( 231 a + 199\bigr] \)

Rank

Rank: \( 1 \)

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