Elliptic curve isogeny class 180.1-c over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-180.1-c
• Conductor: 180.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 180.1-c over \(\Q(\sqrt{10}) \)

Isogeny class 180.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
180.1-c1	\( \bigl[0\) , \( a\) , \( 0\) , \( 8 a - 18\) , \( -2 a - 8\bigr] \)
180.1-c2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -a - 6\) , \( -20 a + 61\bigr] \)
180.1-c3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 4 a - 11\) , \( -11 a + 25\bigr] \)
180.1-c4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 49 a - 236\) , \( -578 a + 1375\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph