Elliptic curve isogeny class 1936.1-b over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-1936.1-b
• Conductor: 1936.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1936.1-b over \(\Q(\sqrt{13}) \)

Isogeny class 1936.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1936.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 105 a - 245\) , \( -1224 a + 2822\bigr] \)
1936.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a - 215\) , \( 664 a + 1038\bigr] \)
1936.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a - 280\) , \( -972 a + 2241\bigr] \)
1936.1-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 120 a - 335\) , \( -664 a + 1702\bigr] \)

Rank

Rank: \( 0 \)

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