Properties

Label 3330.m
Number of curves $4$
Conductor $3330$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3330.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3330.m1 3330s4 \([1, -1, 1, -94388, 5005847]\) \(127568139540190201/59114336463360\) \(43094351281789440\) \([6]\) \(48384\) \(1.8864\)  
3330.m2 3330s2 \([1, -1, 1, -47813, -4011883]\) \(16581570075765001/998001000\) \(727542729000\) \([2]\) \(16128\) \(1.3371\)  
3330.m3 3330s1 \([1, -1, 1, -2813, -69883]\) \(-3375675045001/999000000\) \(-728271000000\) \([2]\) \(8064\) \(0.99057\) \(\Gamma_0(N)\)-optimal
3330.m4 3330s3 \([1, -1, 1, 20812, 582167]\) \(1367594037332999/995878502400\) \(-725995428249600\) \([6]\) \(24192\) \(1.5399\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3330.m have rank \(0\).

Complex multiplication

The elliptic curves in class 3330.m do not have complex multiplication.

Modular form 3330.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 4q^{7} + q^{8} - q^{10} - 6q^{11} + 2q^{13} - 4q^{14} + q^{16} + 6q^{17} + 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.