Elliptic curve isogeny class 32400.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-32400.1-a
• Conductor: 32400.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 32400.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 32400.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
32400.1-a1	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -22 i - 9\) , \( -45 i + 20\bigr] \)
32400.1-a2	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -82 i - 129\) , \( 455 i + 540\bigr] \)
32400.1-a3	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 999 i + 411\) , \( 14428 i + 39825\bigr] \)
32400.1-a4	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -441 i + 831\) , \( 8688 i + 7645\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph