Elliptic curve isogeny class 30492.5-o over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-30492.5-o
• Conductor: 30492.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 30492.5-o over \(\Q(\sqrt{-7}) \)

Isogeny class 30492.5-o contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
30492.5-o1	\( \bigl[1\) , \( a\) , \( a\) , \( -38 a + 390\) , \( 2189 a - 538\bigr] \)
30492.5-o2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -97\) , \( 1337\bigr] \)
30492.5-o3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -3507\) , \( 6507\bigr] \)
30492.5-o4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 37 a + 352\) , \( -2190 a + 1651\bigr] \)
30492.5-o5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -2517\) , \( 48285\bigr] \)
30492.5-o6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -40247\) , \( 3104415\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph