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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-450.1-a
• Conductor: 450.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
450.1-a1	\( \bigl[a\) , \( 1\) , \( a\) , \( -13\) , \( -37\bigr] \)
450.1-a2	\( \bigl[a\) , \( 1\) , \( a\) , \( -113\) , \( 2063\bigr] \)
450.1-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( 7600 a - 28913\) , \( -733040 a + 2309263\bigr] \)
450.1-a4	\( \bigl[a\) , \( 1\) , \( a\) , \( 500 a - 1813\) , \( 12460 a - 40637\bigr] \)
450.1-a5	\( \bigl[a\) , \( 1\) , \( a\) , \( -3313\) , \( 69263\bigr] \)
450.1-a6	\( \bigl[a\) , \( 1\) , \( a\) , \( -213\) , \( -1437\bigr] \)
450.1-a7	\( \bigl[a\) , \( 1\) , \( a\) , \( -7600 a - 28913\) , \( 733040 a + 2309263\bigr] \)
450.1-a8	\( \bigl[a\) , \( 1\) , \( a\) , \( -500 a - 1813\) , \( -12460 a - 40637\bigr] \)

Rank

Rank: \( 0 \)

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