Elliptic curve isogeny class 441.1-c over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-441.1-c
• Conductor: 441.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 441.1-c over \(\Q(\sqrt{10}) \)

Isogeny class 441.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
441.1-c1	\( \bigl[a\) , \( 1\) , \( a\) , \( -137\) , \( -1873\bigr] \)
441.1-c2	\( \bigl[a\) , \( 1\) , \( a\) , \( 3\) , \( 3\bigr] \)
441.1-c3	\( \bigl[a\) , \( 1\) , \( a\) , \( -17\) , \( -25\bigr] \)
441.1-c4	\( \bigl[a\) , \( 1\) , \( a\) , \( -157\) , \( 563\bigr] \)
441.1-c5	\( \bigl[a\) , \( 1\) , \( a\) , \( -197\) , \( -1285\bigr] \)
441.1-c6	\( \bigl[a\) , \( 1\) , \( a\) , \( -3137\) , \( -71257\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph