Elliptic curve isogeny class 12337.5-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12337.5-c
• Conductor: 12337.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 12337.5-c over \(\Q(\sqrt{-3}) \)

Isogeny class 12337.5-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
12337.5-c1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 180 a - 151\) , \( -1007 a + 266\bigr] \)
12337.5-c2	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -40 a + 79\) , \( -147 a - 80\bigr] \)
12337.5-c3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -5 a + 4\) , \( -5 a + 2\bigr] \)
12337.5-c4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 140 a - 186\) , \( -1021 a - 380\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph