Properties

Label 327990.ba
Number of curves $4$
Conductor $327990$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 327990.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
327990.ba1 327990ba3 \([1, 1, 1, -72770486, 238905369683]\) \(71647584155243142409/10140000\) \(6031508474940000\) \([2]\) \(32112640\) \(2.8809\)  
327990.ba2 327990ba4 \([1, 1, 1, -5221366, 2553636179]\) \(26465989780414729/10571870144160\) \(6288394908329999955360\) \([2]\) \(32112640\) \(2.8809\)  
327990.ba3 327990ba2 \([1, 1, 1, -4548566, 3730767059]\) \(17496824387403529/6580454400\) \(3914207739897062400\) \([2, 2]\) \(16056320\) \(2.5343\)  
327990.ba4 327990ba1 \([1, 1, 1, -242646, 75902163]\) \(-2656166199049/2658140160\) \(-1581123757654671360\) \([2]\) \(8028160\) \(2.1878\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 327990.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 327990.ba do not have complex multiplication.

Modular form 327990.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 4q^{7} + q^{8} + q^{9} - q^{10} - q^{12} - q^{13} + 4q^{14} + q^{15} + q^{16} + 2q^{17} + q^{18} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.