Elliptic curve isogeny class 5202.5-i over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5202.5-i
• Conductor: 5202.5
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 5202.5-i over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.5-i contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
5202.5-i1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \)
5202.5-i2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 4305 a - 924\) , \( -137739 a - 127314\bigr] \)
5202.5-i3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -4305 a - 924\) , \( 137739 a - 127314\bigr] \)
5202.5-i4	\( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \)
5202.5-i5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \)
5202.5-i6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \)
5202.5-i7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \)
5202.5-i8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 8 & 4 & 8 & 2 & 4 \\ 2 & 1 & 4 & 16 & 8 & 16 & 4 & 8 \\ 2 & 4 & 1 & 16 & 8 & 16 & 4 & 8 \\ 8 & 16 & 16 & 1 & 2 & 4 & 4 & 8 \\ 4 & 8 & 8 & 2 & 1 & 2 & 2 & 4 \\ 8 & 16 & 16 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 4 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 8 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph