Properties

Label 333795ca
Number of curves $4$
Conductor $333795$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ca1")
 
E.isogeny_class()
 

Elliptic curves in class 333795ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333795.ca3 333795ca1 \([1, 0, 1, -58818, 5481583]\) \(932288503609/779625\) \(18818252231625\) \([2]\) \(1327104\) \(1.4751\) \(\Gamma_0(N)\)-optimal
333795.ca2 333795ca2 \([1, 0, 1, -71823, 2875381]\) \(1697509118089/833765625\) \(20125075303265625\) \([2, 2]\) \(2654208\) \(1.8216\)  
333795.ca4 333795ca3 \([1, 0, 1, 261972, 22101973]\) \(82375335041831/56396484375\) \(-1361274032958984375\) \([2]\) \(5308416\) \(2.1682\)  
333795.ca1 333795ca4 \([1, 0, 1, -613698, -183096119]\) \(1058993490188089/13182390375\) \(318190857261498375\) \([2]\) \(5308416\) \(2.1682\)  

Rank

sage: E.rank()
 

The elliptic curves in class 333795ca have rank \(0\).

Complex multiplication

The elliptic curves in class 333795ca do not have complex multiplication.

Modular form 333795.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{7} - 3 q^{8} + q^{9} + q^{10} + q^{11} - q^{12} - 2 q^{13} - q^{14} + q^{15} - q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) 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 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.