Elliptic curve isogeny class 34.1-c over number field \(\Q(\sqrt{51}) \)

• Base field: \(\Q(\sqrt{51}) \)
• Label: 2.2.204.1-34.1-c
• Conductor: 34.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{51}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 51 \); class number \(2\).

Elliptic curves in class 34.1-c over \(\Q(\sqrt{51}) \)

Isogeny class 34.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
34.1-c1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -27\) , \( -27\bigr] \)
34.1-c2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1017\) , \( 8883\bigr] \)
34.1-c3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -387\) , \( -2835\bigr] \)
34.1-c4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -927\) , \( 11097\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph