Properties

Label 310464.kg
Number of curves $4$
Conductor $310464$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("kg1")
 
E.isogeny_class()
 

Elliptic curves in class 310464.kg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
310464.kg1 310464kg4 \([0, 0, 0, -398890380, 3066182254352]\) \(312196988566716625/25367712678\) \(570344161944425473769472\) \([2]\) \(42467328\) \(3.6035\)  
310464.kg2 310464kg3 \([0, 0, 0, -23228940, 54729886736]\) \(-61653281712625/21875235228\) \(-491822532910936381980672\) \([2]\) \(21233664\) \(3.2570\)  
310464.kg3 310464kg2 \([0, 0, 0, -10245900, -6331269616]\) \(5290763640625/2291573592\) \(51521618699059627819008\) \([2]\) \(14155776\) \(3.0542\)  
310464.kg4 310464kg1 \([0, 0, 0, 2172660, -732982768]\) \(50447927375/39517632\) \(-888477845486429011968\) \([2]\) \(7077888\) \(2.7077\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 310464.kg have rank \(1\).

Complex multiplication

The elliptic curves in class 310464.kg do not have complex multiplication.

Modular form 310464.2.a.kg

sage: E.q_eigenform(10)
 
\(q + q^{11} + 2 q^{13} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.