Elliptic curve isogeny class 784.4-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-784.4-a
• Conductor: 784.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 784.4-a over \(\Q(\sqrt{-7}) \)

Isogeny class 784.4-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
784.4-a1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -149 a - 448\) , \( -1964 a - 3504\bigr] \)
784.4-a2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -14 a + 96\) , \( 287 a + 36\bigr] \)
784.4-a3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -9 a - 28\) , \( -32 a - 60\bigr] \)
784.4-a4	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 3 a + 12\) , \( 26 a - 40\bigr] \)
784.4-a5	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -54 a + 66\) , \( 120 a + 304\bigr] \)
784.4-a6	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 16 a - 4\) , \( 8 a + 24\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 8 & 4 & 2 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 8 & 2 & 1 & 8 & 4 \\ 8 & 4 & 4 & 8 & 1 & 2 \\ 4 & 2 & 2 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph