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

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

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

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

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

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

Curve label	Weierstrass Coefficients
31752.1-e1	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i - 3\) , \( 5 i\bigr] \)
31752.1-e2	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 132\) , \( -400 i\bigr] \)
31752.1-e3	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 42\) , \( 122 i\bigr] \)
31752.1-e4	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 672\) , \( 7052 i\bigr] \)

Rank

Rank: \( 1 \)

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