Elliptic curve isogeny class 1575.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-1575.1-a
• Conductor: 1575.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 1575.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 1575.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1575.1-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 17\) , \( -37\bigr] \)
1575.1-a2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -8\) , \( -7\bigr] \)
1575.1-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -3\) , \( 1\bigr] \)
1575.1-a4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -113\) , \( -469\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph