Elliptic curve isogeny class 2500.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-2500.3-a
• Conductor: 2500.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 2500.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 2500.3-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
2500.3-a1	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 125 i - 273\) , \( -1164 i + 1625\bigr] \)
2500.3-a2	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -125 i - 273\) , \( 1164 i + 1625\bigr] \)
2500.3-a3	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 1375 i - 23\) , \( 14836 i + 16125\bigr] \)
2500.3-a4	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -1375 i - 23\) , \( -14836 i + 16125\bigr] \)
2500.3-a5	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 227\) , \( -1961 i\bigr] \)
2500.3-a6	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -23\) , \( 39 i\bigr] \)
2500.3-a7	\( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -62\bigr] \)
2500.3-a8	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1033\) , \( 12438\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph