Properties

Label 38088.g
Number of curves $6$
Conductor $38088$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38088.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38088.g1 38088i6 \([0, 0, 0, -1829811, -952700434]\) \(3065617154/9\) \(1989147581908992\) \([2]\) \(360448\) \(2.1648\)  
38088.g2 38088i4 \([0, 0, 0, -306291, 65239454]\) \(28756228/3\) \(331524596984832\) \([2]\) \(180224\) \(1.8183\)  
38088.g3 38088i3 \([0, 0, 0, -115851, -14478730]\) \(1556068/81\) \(8951164118590464\) \([2, 2]\) \(180224\) \(1.8183\)  
38088.g4 38088i2 \([0, 0, 0, -20631, 851690]\) \(35152/9\) \(248643447738624\) \([2, 2]\) \(90112\) \(1.4717\)  
38088.g5 38088i1 \([0, 0, 0, 3174, 85169]\) \(2048/3\) \(-5180071827888\) \([2]\) \(45056\) \(1.1251\) \(\Gamma_0(N)\)-optimal
38088.g6 38088i5 \([0, 0, 0, 74589, -57403906]\) \(207646/6561\) \(-1450088587211655168\) \([2]\) \(360448\) \(2.1648\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38088.g have rank \(1\).

Complex multiplication

The elliptic curves in class 38088.g do not have complex multiplication.

Modular form 38088.2.a.g

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + 4q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.