Elliptic curve isogeny class 3362.1-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3362.1-c
• Conductor: 3362.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 3362.1-c over \(\Q(\sqrt{2}) \)

Isogeny class 3362.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3362.1-c1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 6 a + 3\) , \( -3071 a - 4348\bigr] \)
3362.1-c2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( 0\bigr] \)
3362.1-c3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -12\) , \( -16\bigr] \)
3362.1-c4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -8 a + 3\) , \( 3070 a - 4348\bigr] \)

Rank

Rank: \( 2 \)

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