Properties

Label 1200.g
Number of curves $4$
Conductor $1200$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1200.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.g1 1200m4 \([0, -1, 0, -13248, -580608]\) \(502270291349/1889568\) \(967458816000\) \([2]\) \(1920\) \(1.1592\)  
1200.g2 1200m2 \([0, -1, 0, -848, 9792]\) \(131872229/18\) \(9216000\) \([2]\) \(384\) \(0.35445\)  
1200.g3 1200m3 \([0, -1, 0, -448, -17408]\) \(-19465109/248832\) \(-127401984000\) \([2]\) \(960\) \(0.81260\)  
1200.g4 1200m1 \([0, -1, 0, -48, 192]\) \(-24389/12\) \(-6144000\) \([2]\) \(192\) \(0.0078760\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1200.g have rank \(1\).

Complex multiplication

The elliptic curves in class 1200.g do not have complex multiplication.

Modular form 1200.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.