Elliptic curve isogeny class 13122.1-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-13122.1-c
• Conductor: 13122.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 13122.1-c over \(\Q(\sqrt{-1}) \)

Isogeny class 13122.1-c contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
13122.1-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -9695\) , \( -364985\bigr] \)
13122.1-c2	\( \bigl[i\) , \( 1\) , \( i\) , \( -4\) , \( -5\bigr] \)
13122.1-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -697\bigr] \)
13122.1-c4	\( \bigl[i\) , \( 1\) , \( i\) , \( 26\) , \( -1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 21 & 3 & 7 \\ 21 & 1 & 7 & 3 \\ 3 & 7 & 1 & 21 \\ 7 & 3 & 21 & 1 \end{array}\right)\)

Isogeny graph