Properties

Label 4600.g
Number of curves $2$
Conductor $4600$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4600.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4600.g1 4600i2 \([0, 0, 0, -875, 7750]\) \(2315250/529\) \(16928000000\) \([2]\) \(3456\) \(0.67517\)  
4600.g2 4600i1 \([0, 0, 0, 125, 750]\) \(13500/23\) \(-368000000\) \([2]\) \(1728\) \(0.32860\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4600.g have rank \(0\).

Complex multiplication

The elliptic curves in class 4600.g do not have complex multiplication.

Modular form 4600.2.a.g

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.