Elliptic curve isogeny class 36864.7-s over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36864.7-s
• Conductor: 36864.7
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 36864.7-s over \(\Q(\sqrt{-7}) \)

Isogeny class 36864.7-s contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
36864.7-s1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 10\) , \( -2 a + 6\bigr] \)
36864.7-s2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 145\) , \( -461 a + 303\bigr] \)