Elliptic curve isogeny class 392.1-c over number field \(\Q(\sqrt{11}) \)

• Base field: \(\Q(\sqrt{11}) \)
• Label: 2.2.44.1-392.1-c
• Conductor: 392.1
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 392.1-c over \(\Q(\sqrt{11}) \)

Isogeny class 392.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
392.1-c1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 18 a + 61\) , \( 342 a + 1134\bigr] \)
392.1-c2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -882 a - 2924\) , \( -22998 a - 76276\bigr] \)
392.1-c3	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 287 a - 940\) , \( -4674 a + 15516\bigr] \)
392.1-c4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 4487 a - 14870\) , \( -300704 a + 997336\bigr] \)

Rank

Rank: \( 0 \)

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