Elliptic curve isogeny class 121.1-c over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-121.1-c
• Conductor: 121.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 121.1-c over \(\Q(\sqrt{10}) \)

Isogeny class 121.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
121.1-c1	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 3 a - 12\) , \( -17 a + 51\bigr] \)
121.1-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 86 a - 272\) , \( -800 a + 2530\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph