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Properties

Label 438.g
Number of curves $4$
Conductor $438$
CM no
Rank $0$
Graph

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

Elliptic curves in class 438.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
438.g1 438a3 \([1, 0, 0, -72938, -7587996]\) \(42912679782639390625/224073792\) \(224073792\) \([2]\) \(864\) \(1.2196\)  
438.g2 438a4 \([1, 0, 0, -72898, -7596724]\) \(-42842117160045582625/98064578635272\) \(-98064578635272\) \([2]\) \(1728\) \(1.5661\)  
438.g3 438a1 \([1, 0, 0, -938, -9564]\) \(91276959390625/13950517248\) \(13950517248\) \([6]\) \(288\) \(0.67027\) \(\Gamma_0(N)\)-optimal
438.g4 438a2 \([1, 0, 0, 1622, -52060]\) \(471910376801375/1450009133568\) \(-1450009133568\) \([6]\) \(576\) \(1.0168\)  

Rank

sage: E.rank()
 

The elliptic curves in class 438.g have rank \(0\).

Complex multiplication

The elliptic curves in class 438.g do not have complex multiplication.

Modular form 438.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} + q^{12} - 4 q^{13} + 2 q^{14} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.