Elliptic curve isogeny class 51.1-c over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-51.1-c
• Conductor: 51.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 51.1-c over \(\Q(\sqrt{13}) \)

Isogeny class 51.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
51.1-c1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -6 a + 6\) , \( -3 a\bigr] \)
51.1-c2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -16 a - 69\) , \( -78 a - 198\bigr] \)