Elliptic curve isogeny class 15488.20-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15488.20-a
• Conductor: 15488.20
• Rank: \( 1 \)

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

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

Elliptic curves in class 15488.20-a over \(\Q(\sqrt{-7}) \)

Isogeny class 15488.20-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
15488.20-a1	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 4 a - 53\) , \( 50 a + 95\bigr] \)
15488.20-a2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -a + 7\) , \( -3 a - 1\bigr] \)
15488.20-a3	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -6 a + 17\) , \( 12 a + 9\bigr] \)
15488.20-a4	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -96 a + 247\) , \( 774 a + 643\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph