Elliptic curve isogeny class 129792.1-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-129792.1-d
• Conductor: 129792.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 129792.1-d over \(\Q(\sqrt{-3}) \)

Isogeny class 129792.1-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
129792.1-d1	\( \bigl[0\) , \( a\) , \( 0\) , \( 115 a + 10\) , \( 107 a - 577\bigr] \)
129792.1-d2	\( \bigl[0\) , \( a\) , \( 0\) , \( 120\) , \( -548 a + 292\bigr] \)
129792.1-d3	\( \bigl[0\) , \( a\) , \( 0\) , \( 110 a + 125\) , \( 6369 a + 2934\bigr] \)
129792.1-d4	\( \bigl[0\) , \( a\) , \( 0\) , \( 5 a + 5\) , \( -6 a - 6\bigr] \)
129792.1-d5	\( \bigl[0\) , \( a\) , \( 0\) , \( -30 a - 35\) , \( -115 a - 34\bigr] \)
129792.1-d6	\( \bigl[0\) , \( a\) , \( 0\) , \( -170 a - 195\) , \( 1465 a + 806\bigr] \)
129792.1-d7	\( \bigl[0\) , \( a\) , \( 0\) , \( -450 a - 515\) , \( -7471 a - 3226\bigr] \)
129792.1-d8	\( \bigl[0\) , \( a\) , \( 0\) , \( -2690 a - 3075\) , \( 102481 a + 50198\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 16 & 2 & 4 & 8 & 8 & 16 \\ 4 & 1 & 16 & 2 & 4 & 8 & 8 & 16 \\ 16 & 16 & 1 & 8 & 4 & 2 & 8 & 4 \\ 2 & 2 & 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 8 & 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 8 & 8 & 4 & 2 & 4 & 1 & 8 \\ 16 & 16 & 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph