Elliptic curve isogeny class 18432.7-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-18432.7-b
• Conductor: 18432.7
• Rank: \( 0 \)

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

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

Elliptic curves in class 18432.7-b over \(\Q(\sqrt{-7}) \)

Isogeny class 18432.7-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
18432.7-b1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a - 10\) , \( -8 a - 8\bigr] \)
18432.7-b2	\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a + 5\) , \( -3 a + 14\bigr] \)
18432.7-b3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -27 a + 25\) , \( 41 a - 115\bigr] \)
18432.7-b4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -32 a - 160\) , \( -296 a - 680\bigr] \)

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