Elliptic curve isogeny class 11250.3-g over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-11250.3-g
• Conductor: 11250.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 11250.3-g over \(\Q(\sqrt{-1}) \)

Isogeny class 11250.3-g contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
11250.3-g1	\( \bigl[i\) , \( -1\) , \( i\) , \( -337\) , \( 7969\bigr] \)
11250.3-g2	\( \bigl[i\) , \( -1\) , \( i\) , \( 38\) , \( -281\bigr] \)
11250.3-g3	\( \bigl[i\) , \( -1\) , \( i\) , \( -11337\) , \( 67969\bigr] \)
11250.3-g4	\( \bigl[i\) , \( -1\) , \( i\) , \( -1712\) , \( 24219\bigr] \)
11250.3-g5	\( \bigl[i\) , \( -1\) , \( i\) , \( -462\) , \( -3281\bigr] \)
11250.3-g6	\( \bigl[i\) , \( -1\) , \( i\) , \( -8337\) , \( 295969\bigr] \)
11250.3-g7	\( \bigl[i\) , \( -1\) , \( i\) , \( -7212\) , \( -232781\bigr] \)
11250.3-g8	\( \bigl[i\) , \( -1\) , \( i\) , \( -133337\) , \( 18795969\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph