Elliptic curve isogeny class 23409.2-e over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-23409.2-e
• Conductor: 23409.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 23409.2-e over \(\Q(\sqrt{-1}) \)

Isogeny class 23409.2-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
23409.2-e1	\( \bigl[i\) , \( 1\) , \( 0\) , \( -6\) , \( -377\bigr] \)
23409.2-e2	\( \bigl[i\) , \( 1\) , \( 0\) , \( -6\) , \( 1\bigr] \)
23409.2-e3	\( \bigl[i\) , \( 1\) , \( 0\) , \( -675 i + 354\) , \( 351 i - 7847\bigr] \)
23409.2-e4	\( \bigl[i\) , \( 1\) , \( 0\) , \( 675 i + 354\) , \( -351 i - 7847\bigr] \)
23409.2-e5	\( \bigl[i\) , \( 1\) , \( 0\) , \( -51\) , \( -152\bigr] \)
23409.2-e6	\( \bigl[i\) , \( 1\) , \( 0\) , \( -816\) , \( -9179\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 2 & 2 & 4 \\ 4 & 1 & 8 & 8 & 2 & 4 \\ 2 & 8 & 1 & 4 & 4 & 8 \\ 2 & 8 & 4 & 1 & 4 & 8 \\ 2 & 2 & 4 & 4 & 1 & 2 \\ 4 & 4 & 8 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph