Elliptic curve isogeny class 6084.2-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-6084.2-b
• Conductor: 6084.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-1}) \)

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

Elliptic curves in class 6084.2-b over \(\Q(\sqrt{-1}) \)

Isogeny class 6084.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
6084.2-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -13\) , \( 4\bigr] \)
6084.2-b2	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 187\) , \( 945 i\bigr] \)
6084.2-b3	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 37\) , \( -81 i\bigr] \)
6084.2-b4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -733\) , \( 7888\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph