Properties

Base field 3.3.148.1
Label 3.3.148.1-304.1-g
Conductor 304.1
Rank \( 0 \)

Related objects

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Base field 3.3.148.1

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

Elliptic curves in class 304.1-g over 3.3.148.1

Isogeny class 304.1-g contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
304.1-g1 \( \bigl[a^{2} - 1\) , \( -a^{2} + 2\) , \( a^{2} - 1\) , \( -1037279 a^{2} - 1213704 a + 477990\) , \( 1059093688 a^{2} + 1239231212 a - 488042156\bigr] \)
304.1-g2 \( \bigl[a^{2} - 1\) , \( -a^{2} + 3\) , \( 0\) , \( -a^{2} + 1\) , \( -2 a^{2} + 3\bigr] \)
304.1-g3 \( \bigl[0\) , \( -a\) , \( 0\) , \( -27907 a^{2} - 32654 a + 12860\) , \( -97420996 a^{2} - 113990991 a + 44892679\bigr] \)
304.1-g4 \( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -165965341312 a^{2} - 194193803116 a + 76478676008\) , \( 79041132025753191 a^{2} + 92484960470958028 a - 36423033143090658\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph