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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-50625.3-d
• 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-d over \(\Q(\sqrt{-1}) \)

Isogeny class 50625.3-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
50625.3-d1	\( \bigl[i + 1\) , \( i\) , \( i\) , \( -338 i + 2531\) , \( -47672 i - 9956\bigr] \)
50625.3-d2	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( 37 i + 280\) , \( 1953 i - 394\bigr] \)
50625.3-d3	\( \bigl[i + 1\) , \( i\) , \( i\) , \( 37 i - 94\) , \( -422 i - 81\bigr] \)
50625.3-d4	\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -338 i - 845\) , \( 9703 i - 1519\bigr] \)

Rank

Rank: \( 1 \)

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