Properties

Label 1200.n
Number of curves $2$
Conductor $1200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.n1 1200o2 \([0, 1, 0, -1213, 15863]\) \(-30866268160/3\) \(-19200\) \([]\) \(432\) \(0.25522\)  
1200.n2 1200o1 \([0, 1, 0, -13, 23]\) \(-40960/27\) \(-172800\) \([]\) \(144\) \(-0.29409\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1200.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} - 6q^{11} - 5q^{13} + 6q^{17} - 5q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.