Elliptic curve isogeny class 450.1-bh over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-450.1-bh
• Conductor: 450.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 450.1-bh over \(\Q(\sqrt{10}) \)

Isogeny class 450.1-bh contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
450.1-bh1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \)
450.1-bh2	\( \bigl[1\) , \( 0\) , \( 0\) , \( -28\) , \( 272\bigr] \)
450.1-bh3	\( \bigl[1\) , \( 0\) , \( 0\) , \( 1900 a - 7228\) , \( -92580 a + 292272\bigr] \)
450.1-bh4	\( \bigl[1\) , \( 0\) , \( 0\) , \( 125 a - 453\) , \( 1495 a - 4853\bigr] \)
450.1-bh5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -828\) , \( 9072\bigr] \)
450.1-bh6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -53\) , \( -153\bigr] \)
450.1-bh7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1900 a - 7228\) , \( 92580 a + 292272\bigr] \)
450.1-bh8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -125 a - 453\) , \( -1495 a - 4853\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 20 & 4 & 10 & 2 & 20 & 4 \\ 5 & 1 & 4 & 20 & 2 & 10 & 4 & 20 \\ 20 & 4 & 1 & 20 & 2 & 10 & 4 & 5 \\ 4 & 20 & 20 & 1 & 10 & 2 & 5 & 4 \\ 10 & 2 & 2 & 10 & 1 & 5 & 2 & 10 \\ 2 & 10 & 10 & 2 & 5 & 1 & 10 & 2 \\ 20 & 4 & 4 & 5 & 2 & 10 & 1 & 20 \\ 4 & 20 & 5 & 4 & 10 & 2 & 20 & 1 \end{array}\right)\)

Isogeny graph