Elliptic curve isogeny class 1250.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1250.3-a
• Conductor: 1250.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 1250.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 1250.3-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
1250.3-a1	\( \bigl[i\) , \( 0\) , \( i\) , \( -125\) , \( 552\bigr] \)
1250.3-a2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \)
1250.3-a3	\( \bigl[i\) , \( 0\) , \( i\) , \( 0\) , \( 2\bigr] \)
1250.3-a4	\( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph