Elliptic curve isogeny class 8450.5-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-8450.5-a
• Conductor: 8450.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 8450.5-a over \(\Q(\sqrt{-1}) \)

Isogeny class 8450.5-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
8450.5-a1	\( \bigl[i\) , \( 0\) , \( i\) , \( -12\) , \( -156\bigr] \)
8450.5-a2	\( \bigl[i\) , \( 0\) , \( i\) , \( 113\) , \( 4194\bigr] \)
8450.5-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -208\) , \( -1122\bigr] \)
8450.5-a4	\( \bigl[i\) , \( 0\) , \( i\) , \( -370 i + 148\) , \( 732 i - 2932\bigr] \)
8450.5-a5	\( \bigl[i\) , \( 0\) , \( i\) , \( 370 i + 148\) , \( -732 i - 2932\bigr] \)
8450.5-a6	\( \bigl[i\) , \( 0\) , \( i\) , \( 3320 i + 2673\) , \( -25472 i + 103138\bigr] \)
8450.5-a7	\( \bigl[i\) , \( 0\) , \( i\) , \( -3320 i + 2673\) , \( 25472 i + 103138\bigr] \)
8450.5-a8	\( \bigl[1\) , \( 0\) , \( 1\) , \( -33\) , \( 68\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph