Properties

Label 479370z
Number of curves $4$
Conductor $479370$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 479370z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
479370.z3 479370z1 \([1, 0, 1, -26089, 1610012]\) \(3301293169/22800\) \(13561971718800\) \([2]\) \(1548288\) \(1.3534\) \(\Gamma_0(N)\)-optimal
479370.z2 479370z2 \([1, 0, 1, -42909, -724604]\) \(14688124849/8122500\) \(4831452424822500\) \([2, 2]\) \(3096576\) \(1.7000\)  
479370.z4 479370z3 \([1, 0, 1, 167341, -5686504]\) \(871257511151/527800050\) \(-313947778564966050\) \([2]\) \(6193152\) \(2.0466\)  
479370.z1 479370z4 \([1, 0, 1, -522279, -145110848]\) \(26487576322129/44531250\) \(26488226013281250\) \([2]\) \(6193152\) \(2.0466\)  

Rank

sage: E.rank()
 

The elliptic curves in class 479370z have rank \(1\).

Complex multiplication

The elliptic curves in class 479370z do not have complex multiplication.

Modular form 479370.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} + 2q^{13} - q^{15} + q^{16} - 2q^{17} - q^{18} + q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.