Elliptic curve isogeny class 15488.5-f over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15488.5-f
• Conductor: 15488.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 15488.5-f over \(\Q(\sqrt{-7}) \)

Isogeny class 15488.5-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
15488.5-f1	\( \bigl[a\) , \( a\) , \( a\) , \( -16 a + 45\) , \( 73 a + 50\bigr] \)
15488.5-f2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -10 a - 4\) , \( 0\bigr] \)
15488.5-f3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 40 a + 16\) , \( 10 a - 124\bigr] \)
15488.5-f4	\( \bigl[a\) , \( 1\) , \( a\) , \( 20 a - 42\) , \( -68 a + 79\bigr] \)

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