Elliptic curve isogeny class 31752.1-f over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-31752.1-f
• Conductor: 31752.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 31752.1-f over \(\Q(\sqrt{-1}) \)

Isogeny class 31752.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
31752.1-f1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -66\) , \( -1339\bigr] \)
31752.1-f2	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 882\) , \( 1652 i\bigr] \)
31752.1-f3	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 567\) , \( -4900 i\bigr] \)
31752.1-f4	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 9072\) , \( -328090 i\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph