Elliptic curve isogeny class 1872.1-c over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1872.1-c
• Conductor: 1872.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1872.1-c over \(\Q(\sqrt{13}) \)

Isogeny class 1872.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1872.1-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 25 a - 50\) , \( -83 a + 210\bigr] \)
1872.1-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -20\) , \( -24\bigr] \)
1872.1-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 6\bigr] \)
1872.1-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -25 a - 25\) , \( 83 a + 127\bigr] \)

Rank

Rank: \( 1 \)

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