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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-39204.5-i
• 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-i over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
39204.5-i1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -1607 a + 6856\) , \( -323130 a + 66327\bigr] \)
39204.5-i2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 178 a + 583\) , \( -12028 a + 9317\bigr] \)
39204.5-i3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 2788 a - 1754\) , \( -53355 a - 24995\bigr] \)
39204.5-i4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -25097 a + 9313\) , \( -1415469 a + 2106123\bigr] \)

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