Elliptic curve isogeny class 25088.4-j over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-25088.4-j
• Conductor: 25088.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 25088.4-j over \(\Q(\sqrt{-7}) \)

Isogeny class 25088.4-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
25088.4-j1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 5\) , \( 141 a - 171\bigr] \)
25088.4-j2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 96 a - 80\) , \( 384 a + 96\bigr] \)
25088.4-j3	\( \bigl[0\) , \( a\) , \( 0\) , \( 12 a - 136\) , \( 36 a - 600\bigr] \)
25088.4-j4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 282 a - 565\) , \( 3221 a - 4091\bigr] \)

Rank

Rank: \( 1 \)

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