Elliptic curve isogeny class 1458.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1458.1-a
• Conductor: 1458.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1458.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 1458.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
1458.1-a1	\( \bigl[1\) , \( -1\) , \( i + 1\) , \( 283 i + 133\) , \( -338 i - 2152\bigr] \)
1458.1-a2	\( \bigl[1\) , \( -1\) , \( i + 1\) , \( 13 i - 2\) , \( 13 i + 8\bigr] \)
1458.1-a3	\( \bigl[1\) , \( -1\) , \( i + 1\) , \( -2 i - 2\) , \( i + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph