Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.p1 1200r1 \([0, 1, 0, -133, 563]\) \(-102400/3\) \(-7680000\) \([]\) \(240\) \(0.10005\) \(\Gamma_0(N)\)-optimal
1200.p2 1200r2 \([0, 1, 0, 667, -29037]\) \(20480/243\) \(-388800000000\) \([]\) \(1200\) \(0.90477\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1200.2.a.p

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 LMFDB 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 LMFDB labels.