LMFDB - Elliptic curve isogeny class 46.4-c over number field \(\Q(\sqrt{2}, \sqrt{3})\)

Base field \(\Q(\sqrt{2}, \sqrt{3})\)

Generator \(a\), with minimal polynomial \( x^{4} - 4 x^{2} + 1 \); class number \(1\).

Isogeny class 46.4-c contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
46.4-c1	\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 3 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -118 a^{3} - 475 a^{2} - 189 a - 68\) , \( 4371 a^{3} + 10194 a^{2} - 170 a - 1339\bigr] \)
46.4-c2	\( \bigl[a^{3} - 4 a\) , \( a^{2} - a - 3\) , \( a^{2} + a - 2\) , \( -a + 2\) , \( 3 a^{3} - 7 a^{2} + 1\bigr] \)

Rank: \( 0 \)

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

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