Properties

Label 39600.c
Number of curves $4$
Conductor $39600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 39600.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39600.c1 39600v4 \([0, 0, 0, -270075, 53932250]\) \(186779563204/360855\) \(4209012720000000\) \([2]\) \(393216\) \(1.8869\)  
39600.c2 39600v3 \([0, 0, 0, -225075, -40882750]\) \(108108036004/658845\) \(7684768080000000\) \([2]\) \(393216\) \(1.8869\)  
39600.c3 39600v2 \([0, 0, 0, -22575, 224750]\) \(436334416/245025\) \(714492900000000\) \([2, 2]\) \(196608\) \(1.5404\)  
39600.c4 39600v1 \([0, 0, 0, 5550, 27875]\) \(103737344/61875\) \(-11276718750000\) \([2]\) \(98304\) \(1.1938\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 39600.c have rank \(0\).

Complex multiplication

The elliptic curves in class 39600.c do not have complex multiplication.

Modular form 39600.2.a.c

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