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Properties

Label 1650.m
Number of curves $4$
Conductor $1650$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1650.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1650.m1 1650m3 \([1, 1, 1, -2013, -35469]\) \(57736239625/255552\) \(3993000000\) \([2]\) \(1728\) \(0.69464\)  
1650.m2 1650m4 \([1, 1, 1, -1013, -69469]\) \(-7357983625/127552392\) \(-1993006125000\) \([2]\) \(3456\) \(1.0412\)  
1650.m3 1650m1 \([1, 1, 1, -138, 531]\) \(18609625/1188\) \(18562500\) \([2]\) \(576\) \(0.14534\) \(\Gamma_0(N)\)-optimal
1650.m4 1650m2 \([1, 1, 1, 112, 2531]\) \(9938375/176418\) \(-2756531250\) \([2]\) \(1152\) \(0.49191\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1650.m have rank \(0\).

Complex multiplication

The elliptic curves in class 1650.m do not have complex multiplication.

Modular form 1650.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{11} - q^{12} + 4 q^{13} - 2 q^{14} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.