Elliptic curve isogeny class 10170.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-10170.1-a
• Conductor: 10170.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 10170.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 10170.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
10170.1-a1	\( \bigl[i\) , \( i + 1\) , \( i\) , \( 130 i - 3369\) , \( -5431 i + 74351\bigr] \)
10170.1-a2	\( \bigl[i\) , \( i + 1\) , \( i\) , \( 10 i - 209\) , \( -119 i + 1135\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph