Properties

Base field 3.3.148.1
Label 3.3.148.1-361.2-a
Conductor 361.2
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 361.2-a over 3.3.148.1

Isogeny class 361.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
361.2-a1 \( \bigl[a^{2} - a - 2\) , \( a\) , \( a^{2} - 2\) , \( -a^{2} + 12 a - 21\) , \( -3 a^{2} - 29 a + 75\bigr] \)
361.2-a2 \( \bigl[a^{2} - a - 2\) , \( 1\) , \( 1\) , \( -135415 a^{2} - 158416 a + 62393\) , \( 49915104 a^{2} + 58405091 a - 23001468\bigr] \)
361.2-a3 \( \bigl[0\) , \( a^{2} - 2\) , \( a^{2} - 2\) , \( -25887000022915 a^{2} - 30290028906100 a + 11929017660105\) , \( 153975054462382521802 a^{2} + 180164130503941360671 a - 70953418405815227560\bigr] \)
361.2-a4 \( \bigl[0\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -4352941 a^{2} - 5093316 a + 2005886\) , \( -189816234978 a^{2} - 222101411490 a + 87469433199\bigr] \)

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