Elliptic curve isogeny class 256.1-c over number field \(\Q(\sqrt{13}) \)

• Base field: \(\Q(\sqrt{13}) \)
• Label: 2.2.13.1-256.1-c
• Conductor: 256.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 256.1-c over \(\Q(\sqrt{13}) \)

Isogeny class 256.1-c contains 6 curves linked by isogenies of degrees dividing 45.

Curve label	Weierstrass Coefficients
256.1-c1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -456 a + 24\) , \( 2400 a + 6788\bigr] \)
256.1-c2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -24 a - 32\) , \( -96 a - 124\bigr] \)
256.1-c3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1189 a - 2774\) , \( -30433 a + 70154\bigr] \)
256.1-c4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 24 a - 56\) , \( 96 a - 220\bigr] \)
256.1-c5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -11 a + 26\) , \( 79 a - 182\bigr] \)
256.1-c6	\( \bigl[0\) , \( 1\) , \( 0\) , \( 456 a - 432\) , \( -2400 a + 9188\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 45 & 3 & 5 & 15 & 9 \\ 45 & 1 & 15 & 9 & 3 & 5 \\ 3 & 15 & 1 & 15 & 5 & 3 \\ 5 & 9 & 15 & 1 & 3 & 45 \\ 15 & 3 & 5 & 3 & 1 & 15 \\ 9 & 5 & 3 & 45 & 15 & 1 \end{array}\right)\)

Isogeny graph