Elliptic curve isogeny class 5330.7-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-5330.7-b
• Conductor: 5330.7
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 5330.7-b over \(\Q(\sqrt{-1}) \)

Isogeny class 5330.7-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
5330.7-b1	\( \bigl[i\) , \( 0\) , \( 1\) , \( -1291 i - 3744\) , \( -45703 i - 83965\bigr] \)
5330.7-b2	\( \bigl[1\) , \( 0\) , \( i\) , \( -81 i - 234\) , \( 711 i + 1297\bigr] \)
5330.7-b3	\( \bigl[i\) , \( 0\) , \( 1\) , \( -16 i - 44\) , \( -66 i - 124\bigr] \)
5330.7-b4	\( \bigl[1\) , \( 0\) , \( i\) , \( -11 i + 1\) , \( -10 i + 14\bigr] \)