Elliptic curve isogeny class 50625.3-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-50625.3-b
• Conductor: 50625.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 50625.3-b over \(\Q(\sqrt{-1}) \)

Isogeny class 50625.3-b contains 10 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
50625.3-b1	\( \bigl[i\) , \( 1\) , \( i\) , \( -23625 i + 88871\) , \( -9922500 i - 4089872\bigr] \)
50625.3-b2	\( \bigl[i\) , \( 1\) , \( i\) , \( 23625 i + 88871\) , \( 9922500 i - 4089872\bigr] \)
50625.3-b3	\( \bigl[i\) , \( 1\) , \( i\) , \( -24754\) , \( -2820872\bigr] \)
50625.3-b4	\( \bigl[i\) , \( 1\) , \( i\) , \( -4\) , \( 628\bigr] \)
50625.3-b5	\( \bigl[i\) , \( 1\) , \( i\) , \( 7871\) , \( -141122\bigr] \)
50625.3-b6	\( \bigl[i\) , \( 1\) , \( i\) , \( -2254\) , \( -19622\bigr] \)
50625.3-b7	\( \bigl[i\) , \( 1\) , \( i\) , \( -1129\) , \( 14128\bigr] \)
50625.3-b8	\( \bigl[i\) , \( 1\) , \( i\) , \( -30379\) , \( -2044622\bigr] \)
50625.3-b9	\( \bigl[i\) , \( 1\) , \( i\) , \( -18004\) , \( 925378\bigr] \)
50625.3-b10	\( \bigl[i\) , \( 1\) , \( i\) , \( -486004\) , \( -130530872\bigr] \)

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