Elliptic curve isogeny class 25600.7-n over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-25600.7-n
• Conductor: 25600.7
• Rank: \( 1 \)

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

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

Elliptic curves in class 25600.7-n over \(\Q(\sqrt{-7}) \)

Isogeny class 25600.7-n contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
25600.7-n1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 36 a + 36\) , \( -140 a + 420\bigr] \)
25600.7-n2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 4\) , \( 4 a - 12\bigr] \)
25600.7-n3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 1\) , \( 0\bigr] \)
25600.7-n4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 41 a + 41\) , \( -116 a + 348\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph