Elliptic curve isogeny class 115248.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-115248.3-b
• Conductor: 115248.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 115248.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 115248.3-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
115248.3-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5553\) , \( 165894\bigr] \)
115248.3-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 735 a + 3267\) , \( -96285 a + 69315\bigr] \)
115248.3-b3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -9065 a - 653\) , \( -541205 a + 525211\bigr] \)
115248.3-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 9065 a - 9718\) , \( 541205 a - 15994\bigr] \)
115248.3-b5	\( \bigl[0\) , \( -1\) , \( 0\) , \( 327\) , \( 666\bigr] \)
115248.3-b6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1388\) , \( 6840\bigr] \)
115248.3-b7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -735 a + 4002\) , \( 96285 a - 26970\bigr] \)
115248.3-b8	\( \bigl[0\) , \( -1\) , \( 0\) , \( -89588\) , \( 10350936\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 6 & 2 & 2 & 3 & 6 & 6 & 2 \\ 6 & 1 & 3 & 12 & 2 & 4 & 4 & 12 \\ 2 & 3 & 1 & 4 & 6 & 12 & 12 & 4 \\ 2 & 12 & 4 & 1 & 6 & 12 & 3 & 4 \\ 3 & 2 & 6 & 6 & 1 & 2 & 2 & 6 \\ 6 & 4 & 12 & 12 & 2 & 1 & 4 & 3 \\ 6 & 4 & 12 & 3 & 2 & 4 & 1 & 12 \\ 2 & 12 & 4 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph