Elliptic curve isogeny class 4225.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-4225.3-a
• Conductor: 4225.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 4225.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 4225.3-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
4225.3-a1	\( \bigl[i + 1\) , \( -i + 1\) , \( i\) , \( 30270 i + 232\) , \( 1427002 i + 1454927\bigr] \)
4225.3-a2	\( \bigl[i + 1\) , \( -i - 1\) , \( 1\) , \( -731 i - 739\) , \( -11543 i - 5045\bigr] \)
4225.3-a3	\( \bigl[i + 1\) , \( -i - 1\) , \( 1\) , \( 44 i - 64\) , \( -225 i + 206\bigr] \)
4225.3-a4	\( \bigl[i + 1\) , \( -i - 1\) , \( 1\) , \( -7536 i - 124\) , \( 182088 i - 183203\bigr] \)
4225.3-a5	\( \bigl[i + 1\) , \( -i + 1\) , \( i\) , \( -50 i - 8\) , \( -189 i + 40\bigr] \)
4225.3-a6	\( \bigl[i + 1\) , \( -i + 1\) , \( i\) , \( 395 i + 107\) , \( 3005 i + 723\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 6 & 18 & 2 & 9 & 3 \\ 6 & 1 & 3 & 3 & 6 & 2 \\ 18 & 3 & 1 & 9 & 2 & 6 \\ 2 & 3 & 9 & 1 & 18 & 6 \\ 9 & 6 & 2 & 18 & 1 & 3 \\ 3 & 2 & 6 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph