Elliptic curve isogeny class 200.1-e over number field \(\Q(\sqrt{19}) \)

• Base field: \(\Q(\sqrt{19}) \)
• Label: 2.2.76.1-200.1-e
• Conductor: 200.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 200.1-e over \(\Q(\sqrt{19}) \)

Isogeny class 200.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
200.1-e1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -43090 a + 187863\) , \( -19152793 a + 83485155\bigr] \)
200.1-e2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 23210 a - 101132\) , \( -3385427 a + 14756800\bigr] \)
200.1-e3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
200.1-e4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 354710 a - 1546107\) , \( -240133867 a + 1046719325\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph