Elliptic curve isogeny class 18.3-c over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-18.3-c
• Conductor: 18.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 18.3-c over \(\Q(\sqrt{10}) \)

Isogeny class 18.3-c contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
18.3-c1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -6220 a - 19669\) , \( -484078 a - 1530789\bigr] \)
18.3-c2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -25 a - 69\) , \( 104 a + 338\bigr] \)
18.3-c3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 95 a + 231\) , \( -6100 a - 19186\bigr] \)
18.3-c4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 65 a + 206\) , \( 203 a + 642\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph