Elliptic curve isogeny class 9801.3-l over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-9801.3-l
• Conductor: 9801.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 9801.3-l over \(\Q(\sqrt{-11}) \)

Isogeny class 9801.3-l contains 8 curves linked by isogenies of degrees dividing 20.

Curve label	Weierstrass Coefficients
9801.3-l1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -33 a + 523\) , \( -2585 a + 349\bigr] \)
9801.3-l2	\( \bigl[a\) , \( -a\) , \( a\) , \( 31 a + 492\) , \( 2584 a - 2235\bigr] \)
9801.3-l3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -33 a + 28\) , \( -110 a + 250\bigr] \)
9801.3-l4	\( \bigl[a\) , \( -a\) , \( a\) , \( 31 a - 3\) , \( 109 a + 141\bigr] \)
9801.3-l5	\( \bigl[a\) , \( -a\) , \( a\) , \( -464 a + 987\) , \( 802 a - 17976\bigr] \)
9801.3-l6	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 462 a + 523\) , \( -803 a - 17174\bigr] \)
9801.3-l7	\( \bigl[a\) , \( -a\) , \( a\) , \( 526 a + 7917\) , \( 168706 a - 132618\bigr] \)
9801.3-l8	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -528 a + 8443\) , \( -168707 a + 36088\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 5 & 2 & 10 & 10 & 2 & 10 & 2 \\ 5 & 1 & 10 & 2 & 2 & 10 & 2 & 10 \\ 2 & 10 & 1 & 5 & 20 & 4 & 20 & 4 \\ 10 & 2 & 5 & 1 & 4 & 20 & 4 & 20 \\ 10 & 2 & 20 & 4 & 1 & 20 & 4 & 5 \\ 2 & 10 & 4 & 20 & 20 & 1 & 5 & 4 \\ 10 & 2 & 20 & 4 & 4 & 5 & 1 & 20 \\ 2 & 10 & 4 & 20 & 5 & 4 & 20 & 1 \end{array}\right)\)

Isogeny graph