Elliptic curve isogeny class 7056.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-7056.3-b
• Conductor: 7056.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 7056.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 7056.3-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
7056.3-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 228 a - 159\) , \( 1248 a - 174\bigr] \)
7056.3-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 33 a + 6\) , \( 51 a - 111\bigr] \)
7056.3-b3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -147 a + 129\) , \( 115 a - 316\bigr] \)
7056.3-b4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -82 a + 74\) , \( -15 a + 235\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph