Elliptic curve isogeny class 36288.4-f over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36288.4-f
• Conductor: 36288.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 36288.4-f over \(\Q(\sqrt{-7}) \)

Isogeny class 36288.4-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36288.4-f1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 110\bigr] \)
36288.4-f2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 36 a - 87\) , \( -172 a + 266\bigr] \)
36288.4-f3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -36 a - 51\) , \( 172 a + 94\bigr] \)
36288.4-f4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -363\) , \( 2630\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph