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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1458.1-c
• 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-c over \(\Q(\sqrt{-1}) \)

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

Curve label	Weierstrass Coefficients
1458.1-c1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
1458.1-c2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -123\) , \( -667\bigr] \)
1458.1-c3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph