Elliptic curve isogeny class 49500.7-k over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-49500.7-k
• Conductor: 49500.7
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-11}) \)

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

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

Elliptic curves in class 49500.7-k over \(\Q(\sqrt{-11}) \)

Isogeny class 49500.7-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
49500.7-k1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 198 a - 247\) , \( -3210 a + 6515\bigr] \)
49500.7-k2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -8942 a + 6633\) , \( 166474 a - 653913\bigr] \)
49500.7-k3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -2442 a + 633\) , \( -50026 a + 67587\bigr] \)
49500.7-k4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -38182 a + 8713\) , \( -3238110 a + 4806815\bigr] \)