Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-361.1-b
Conductor 361.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Elliptic curves in class 361.1-b over \(\Q(\sqrt{33}) \)

Isogeny class 361.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
361.1-b1 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( -283115 a - 671625\) , \( 138745881 a + 329144261\bigr] \)
361.1-b2 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( -3435 a - 8145\) , \( 194841 a + 462216\bigr] \)
361.1-b3 \( \bigl[0\) , \( -a\) , \( 1\) , \( -245 a + 830\) , \( -351 a + 1182\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph