Elliptic curve isogeny class 7500.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-7500.1-b
• Conductor: 7500.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 7500.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 7500.1-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
7500.1-b1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 337 a\) , \( -7969\bigr] \)
7500.1-b2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 37\) , \( 281\bigr] \)
7500.1-b3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 11337 a\) , \( -67969\bigr] \)
7500.1-b4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1713\) , \( -24219\bigr] \)
7500.1-b5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -463\) , \( 3281\bigr] \)
7500.1-b6	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 8337 a\) , \( -295969\bigr] \)
7500.1-b7	\( \bigl[1\) , \( 1\) , \( 1\) , \( -7213\) , \( 232781\bigr] \)
7500.1-b8	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 133337 a\) , \( -18795969\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph