Elliptic curve isogeny class 39204.6-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39204.6-c
• Conductor: 39204.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 39204.6-c over \(\Q(\sqrt{-7}) \)

Isogeny class 39204.6-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
39204.6-c1	\( \bigl[1\) , \( -1\) , \( a\) , \( -2309 a + 6603\) , \( 110874 a - 62365\bigr] \)
39204.6-c2	\( \bigl[1\) , \( -1\) , \( a\) , \( 2353 a - 108\) , \( 15977 a + 60494\bigr] \)
39204.6-c3	\( \bigl[1\) , \( -1\) , \( a\) , \( 931 a - 1677\) , \( 14178 a - 4981\bigr] \)
39204.6-c4	\( \bigl[1\) , \( -1\) , \( a\) , \( -2435 a - 4086\) , \( 104411 a + 77706\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph