Elliptic curve isogeny class 40000.6-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-40000.6-c
• Conductor: 40000.6
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 40000.6-c over \(\Q(\sqrt{-7}) \)

Isogeny class 40000.6-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
40000.6-c1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -41 a - 253\) , \( -361 a - 1609\bigr] \)
40000.6-c2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -41 a - 3\) , \( 139 a - 109\bigr] \)
40000.6-c3	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 36 a - 12\) , \( 40 a + 144\bigr] \)
40000.6-c4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -666 a - 3\) , \( 8264 a - 6359\bigr] \)