Elliptic curve isogeny class 90000.3-ba over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-90000.3-ba
• Conductor: 90000.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 90000.3-ba over \(\Q(\sqrt{-1}) \)

Isogeny class 90000.3-ba contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
90000.3-ba1	\( \bigl[0\) , \( i\) , \( 0\) , \( -100 i - 67\) , \( 487 i + 75\bigr] \)
90000.3-ba2	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 24 i - 15\) , \( 99 i - 144\bigr] \)
90000.3-ba3	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -351 i - 15\) , \( 1974 i - 1269\bigr] \)
90000.3-ba4	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 399 i - 515\) , \( 4974 i - 3519\bigr] \)