Elliptic curve isogeny class 7056.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-7056.1-b
• Conductor: 7056.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 7056.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 7056.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
7056.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -228 a + 69\) , \( -1248 a + 1074\bigr] \)
7056.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -33 a + 39\) , \( -51 a - 60\bigr] \)
7056.1-b3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 149 a - 19\) , \( 33 a - 220\bigr] \)
7056.1-b4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 84 a - 9\) , \( 98 a + 211\bigr] \)

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