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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15488.20-e
• 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-e over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
15488.20-e1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 4 a - 8\) , \( 0\bigr] \)
15488.20-e2	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5 a - 2\) , \( 3 a - 2\bigr] \)
15488.20-e3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 5 a - 19\) , \( -23 a + 35\bigr] \)
15488.20-e4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65 a - 22\) , \( 311 a - 134\bigr] \)

Rank

Rank: \( 1 \)

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