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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-441.1-a
• Conductor: 441.1
• Rank: \( 0 \)

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

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

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

Isogeny class 441.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
441.1-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 542 a - 1716\) , \( -8284 a + 26198\bigr] \)
441.1-a2	\( \bigl[a\) , \( 1\) , \( 1\) , \( 8409 a - 26626\) , \( 755256 a - 2388457\bigr] \)
441.1-a3	\( \bigl[a\) , \( 1\) , \( 1\) , \( 489 a - 1546\) , \( -9921 a + 31373\bigr] \)
441.1-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( 134462 a - 425796\) , \( 47730812 a - 150943402\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph