Properties

Label 61200bp
Number of curves $4$
Conductor $61200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 61200bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61200.m4 61200bp1 \([0, 0, 0, -4553175, 113517481750]\) \(-3579968623693264/1906997690433375\) \(-5560805265303721500000000\) \([2]\) \(10321920\) \(3.4272\) \(\Gamma_0(N)\)-optimal
61200.m3 61200bp2 \([0, 0, 0, -380397675, 2825987238250]\) \(521902963282042184836/6241849278890625\) \(72804929988980250000000000\) \([2, 2]\) \(20643840\) \(3.7738\)  
61200.m2 61200bp3 \([0, 0, 0, -705522675, -2720320136750]\) \(1664865424893526702418/826424127435466125\) \(19278822044814553764000000000\) \([2]\) \(41287680\) \(4.1204\)  
61200.m1 61200bp4 \([0, 0, 0, -6068784675, 181970359029250]\) \(1059623036730633329075378/154307373046875\) \(3599682398437500000000000\) \([2]\) \(41287680\) \(4.1204\)  

Rank

sage: E.rank()
 

The elliptic curves in class 61200bp have rank \(0\).

Complex multiplication

The elliptic curves in class 61200bp do not have complex multiplication.

Modular form 61200.2.a.bp

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - 2 q^{13} - q^{17} - 4 q^{19} + O(q^{20})\) 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.