Elliptic curve isogeny class 1225.3-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-1225.3-c
• Conductor: 1225.3
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).

Elliptic curves in class 1225.3-c over \(\Q(\sqrt{2}) \)

Isogeny class 1225.3-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1225.3-c1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 7 a - 2\) , \( -20 a - 11\bigr] \)
1225.3-c2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -58 a - 87\) , \( -395 a - 524\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph