Elliptic curve isogeny class 2025.2-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-2025.2-c
• Conductor: 2025.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 2025.2-c over \(\Q(\sqrt{-1}) \)

Isogeny class 2025.2-c contains 10 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
2025.2-c1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -945 i + 3555\) , \( 79569 i + 32008\bigr] \)
2025.2-c2	\( \bigl[i\) , \( 1\) , \( 0\) , \( 945 i + 3555\) , \( 79569 i - 32008\bigr] \)
2025.2-c3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \)
2025.2-c4	\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \)
2025.2-c5	\( \bigl[i\) , \( 1\) , \( 0\) , \( 315\) , \( -1066\bigr] \)
2025.2-c6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \)
2025.2-c7	\( \bigl[i\) , \( 1\) , \( 0\) , \( -45\) , \( 104\bigr] \)
2025.2-c8	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \)
2025.2-c9	\( \bigl[i\) , \( 1\) , \( 0\) , \( -720\) , \( 7259\bigr] \)
2025.2-c10	\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 4 & 16 & 16 & 2 & 4 & 8 & 8 & 16 & 16 \\ 4 & 1 & 16 & 16 & 2 & 4 & 8 & 8 & 16 & 16 \\ 16 & 16 & 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 16 & 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 2 & 2 & 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 8 & 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 8 & 8 & 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 16 & 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 16 & 16 & 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph