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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-2025.2-a
• Conductor: 2025.2
• Rank: \( 0 \)

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

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

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

Isogeny class 2025.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
2025.2-a1	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -14 i + 101\) , \( -341 i - 74\bigr] \)
2025.2-a2	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( i + 10\) , \( -9 i + 2\bigr] \)
2025.2-a3	\( \bigl[i + 1\) , \( i\) , \( i\) , \( i - 4\) , \( -5 i - 1\bigr] \)
2025.2-a4	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -14 i - 35\) , \( -98 i + 20\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph