Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.c2 1200k1 \([0, -1, 0, 27, -243]\) \(20480/243\) \(-24883200\) \([]\) \(240\) \(0.10005\) \(\Gamma_0(N)\)-optimal
1200.c1 1200k2 \([0, -1, 0, -3333, 77037]\) \(-102400/3\) \(-120000000000\) \([]\) \(1200\) \(0.90477\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1200.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3q^{7} + q^{9} - 2q^{11} - q^{13} - 2q^{17} + 5q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.