Elliptic curve isogeny class 12996.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12996.1-b
• Conductor: 12996.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 12996.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 12996.1-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
12996.1-b1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -2531 a - 386\) , \( 63043 a - 31836\bigr] \)
12996.1-b2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -26 a + 49\) , \( -347 a + 327\bigr] \)
12996.1-b3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -131 a + 7294\) , \( 381475 a - 31740\bigr] \)
12996.1-b4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 454 a - 581\) , \( -4625 a + 3099\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph