Elliptic curve isogeny class 14450.5-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-14450.5-a
• Conductor: 14450.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 14450.5-a over \(\Q(\sqrt{-1}) \)

Isogeny class 14450.5-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
14450.5-a1	\( \bigl[i\) , \( 0\) , \( i\) , \( -2473\) , \( -52716\bigr] \)
14450.5-a2	\( \bigl[i\) , \( 0\) , \( i\) , \( 6980 i - 1833\) , \( -277616 i - 157004\bigr] \)
14450.5-a3	\( \bigl[i\) , \( 0\) , \( i\) , \( -6980 i - 1833\) , \( 277616 i - 157004\bigr] \)
14450.5-a4	\( \bigl[i\) , \( 0\) , \( i\) , \( 16312\) , \( 159988\bigr] \)
14450.5-a5	\( \bigl[i\) , \( 0\) , \( i\) , \( -4168\) , \( 20724\bigr] \)
14450.5-a6	\( \bigl[i\) , \( 0\) , \( i\) , \( -18880 i + 180152\) , \( 29231744 i + 4657396\bigr] \)
14450.5-a7	\( \bigl[i\) , \( 0\) , \( i\) , \( 18880 i + 180152\) , \( -29231744 i + 4657396\bigr] \)
14450.5-a8	\( \bigl[i\) , \( 0\) , \( i\) , \( -2553\) , \( -49452\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph