Elliptic curve isogeny class 49500.6-i over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-49500.6-i
• Conductor: 49500.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 49500.6-i over \(\Q(\sqrt{-11}) \)

Isogeny class 49500.6-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
49500.6-i1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 6161 a + 4726\) , \( 63553 a - 593817\bigr] \)
49500.6-i2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 351 a - 234\) , \( 6751 a - 19299\bigr] \)
49500.6-i3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -69 a + 46\) , \( -109 a + 441\bigr] \)
49500.6-i4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -309 a + 206\) , \( 1603 a - 3767\bigr] \)
49500.6-i5	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 5101 a - 12234\) , \( 293501 a - 411549\bigr] \)
49500.6-i6	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -4809 a + 3206\) , \( 100903 a - 267467\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 2 & 8 & 4 \\ 4 & 2 & 2 & 1 & 4 & 2 \\ 4 & 2 & 8 & 4 & 1 & 8 \\ 8 & 4 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph