Elliptic curve isogeny class 136900.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-136900.2-c
• Conductor: 136900.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 136900.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 136900.2-c contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
136900.2-c1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 53 a\) , \( 146\bigr] \)
136900.2-c2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 3131 a + 518\) , \( -17740 a + 84482\bigr] \)
136900.2-c3	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -19 a + 18\) , \( 342\bigr] \)
136900.2-c4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 166 a - 167\) , \( -9204\bigr] \)
136900.2-c5	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -519 a - 3132\) , \( 17740 a + 66742\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 3 & 9 & 9 \\ 9 & 1 & 3 & 9 & 9 \\ 3 & 3 & 1 & 3 & 3 \\ 9 & 9 & 3 & 1 & 9 \\ 9 & 9 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph