Elliptic curve isogeny class 4802.1-z over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-4802.1-z
• Conductor: 4802.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4802.1-z over \(\Q(\sqrt{2}) \)

Isogeny class 4802.1-z contains 12 curves linked by isogenies of degrees dividing 36.

Curve label	Weierstrass Coefficients
4802.1-z1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -8355\) , \( 291341\bigr] \)
4802.1-z2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( -111\bigr] \)
4802.1-z3	\( \bigl[1\) , \( 1\) , \( 0\) , \( 220\) , \( 2192\bigr] \)
4802.1-z4	\( \bigl[1\) , \( 1\) , \( 0\) , \( 2695 a - 4435\) , \( 102165 a - 147209\bigr] \)
4802.1-z5	\( \bigl[1\) , \( 1\) , \( 0\) , \( -1740\) , \( 22184\bigr] \)
4802.1-z6	\( \bigl[1\) , \( 1\) , \( 0\) , \( 6370 a - 17420\) , \( -679630 a + 681528\bigr] \)
4802.1-z7	\( \bigl[1\) , \( 1\) , \( 0\) , \( 709520 a - 1137315\) , \( -419287120 a + 611710989\bigr] \)
4802.1-z8	\( \bigl[1\) , \( 1\) , \( 0\) , \( -515\) , \( -4717\bigr] \)
4802.1-z9	\( \bigl[1\) , \( 1\) , \( 0\) , \( -6370 a - 17420\) , \( 679630 a + 681528\bigr] \)
4802.1-z10	\( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \)
4802.1-z11	\( \bigl[1\) , \( 1\) , \( 0\) , \( -2695 a - 4435\) , \( -102165 a - 147209\bigr] \)
4802.1-z12	\( \bigl[1\) , \( 1\) , \( 0\) , \( -709520 a - 1137315\) , \( 419287120 a + 611710989\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 9 & 3 & 36 & 6 & 12 & 4 & 18 & 12 & 2 & 36 & 4 \\ 9 & 1 & 3 & 4 & 6 & 12 & 36 & 2 & 12 & 18 & 4 & 36 \\ 3 & 3 & 1 & 12 & 2 & 4 & 12 & 6 & 4 & 6 & 12 & 12 \\ 36 & 4 & 12 & 1 & 6 & 12 & 36 & 2 & 3 & 18 & 4 & 9 \\ 6 & 6 & 2 & 6 & 1 & 2 & 6 & 3 & 2 & 3 & 6 & 6 \\ 12 & 12 & 4 & 12 & 2 & 1 & 3 & 6 & 4 & 6 & 3 & 12 \\ 4 & 36 & 12 & 36 & 6 & 3 & 1 & 18 & 12 & 2 & 9 & 4 \\ 18 & 2 & 6 & 2 & 3 & 6 & 18 & 1 & 6 & 9 & 2 & 18 \\ 12 & 12 & 4 & 3 & 2 & 4 & 12 & 6 & 1 & 6 & 12 & 3 \\ 2 & 18 & 6 & 18 & 3 & 6 & 2 & 9 & 6 & 1 & 18 & 2 \\ 36 & 4 & 12 & 4 & 6 & 3 & 9 & 2 & 12 & 18 & 1 & 36 \\ 4 & 36 & 12 & 9 & 6 & 12 & 4 & 18 & 3 & 2 & 36 & 1 \end{array}\right)\)

Isogeny graph