Elliptic curve isogeny class 39204.5-f over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39204.5-f
• Conductor: 39204.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 39204.5-f over \(\Q(\sqrt{-7}) \)

Isogeny class 39204.5-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
39204.5-f1	\( \bigl[1\) , \( -1\) , \( a\) , \( -179 a + 762\) , \( 12027 a - 2710\bigr] \)
39204.5-f2	\( \bigl[1\) , \( -1\) , \( a\) , \( 1606 a + 5250\) , \( 323129 a - 256802\bigr] \)
39204.5-f3	\( \bigl[1\) , \( -1\) , \( a\) , \( 25096 a - 15783\) , \( 1415468 a + 690655\bigr] \)
39204.5-f4	\( \bigl[1\) , \( -1\) , \( a\) , \( -2789 a + 1035\) , \( 53354 a - 78349\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph