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Properties

Label 444360cq
Number of curves $4$
Conductor $444360$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 444360cq have rank \(1\).

Complex multiplication

The elliptic curves in class 444360cq do not have complex multiplication.

Modular form 444360.2.a.cq

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{7} + q^{9} + 6 q^{13} + q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 444360cq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
444360.cq3 444360cq1 \([0, 1, 0, -14807415, 21922426638]\) \(151591373397612544/32558203125\) \(77116520701631250000\) \([2]\) \(23654400\) \(2.8108\) \(\Gamma_0(N)\)-optimal
444360.cq2 444360cq2 \([0, 1, 0, -16460540, 16723017888]\) \(13015144447800784/4341909875625\) \(164546173029382734240000\) \([2, 2]\) \(47308800\) \(3.1574\)  
444360.cq4 444360cq3 \([0, 1, 0, 47812960, 115395695088]\) \(79743193254623804/84085819746075\) \(-12746464336285662090931200\) \([2]\) \(94617600\) \(3.5040\)  
444360.cq1 444360cq4 \([0, 1, 0, -107184040, -414685369312]\) \(898353183174324196/29899176238575\) \(4532378762081409247411200\) \([2]\) \(94617600\) \(3.5040\)