Elliptic curve isogeny class 3388.5-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-3388.5-e
• Conductor: 3388.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 3388.5-e over \(\Q(\sqrt{-7}) \)

Isogeny class 3388.5-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3388.5-e1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4\) , \( -89\bigr] \)
3388.5-e2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -604\) , \( 2343\bigr] \)
3388.5-e3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 18 a + 59\) , \( 150 a - 203\bigr] \)
3388.5-e4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -18 a + 77\) , \( -150 a - 53\bigr] \)
3388.5-e5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -324\) , \( -2137\bigr] \)
3388.5-e6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -5164\) , \( -141529\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 2 & 2 & 4 \\ 4 & 1 & 8 & 8 & 2 & 4 \\ 2 & 8 & 1 & 4 & 4 & 8 \\ 2 & 8 & 4 & 1 & 4 & 8 \\ 2 & 2 & 4 & 4 & 1 & 2 \\ 4 & 4 & 8 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph