Properties

Label 1200b
Number of curves $2$
Conductor $1200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.h2 1200b1 \([0, -1, 0, 792, 6912]\) \(27436/27\) \(-54000000000\) \([2]\) \(960\) \(0.74635\) \(\Gamma_0(N)\)-optimal
1200.h1 1200b2 \([0, -1, 0, -4208, 66912]\) \(2060602/729\) \(2916000000000\) \([2]\) \(1920\) \(1.0929\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1200b have rank \(0\).

Complex multiplication

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

Modular form 1200.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{7} + q^{9} - 2q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.