Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1200l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1200.f2 1200l1 \([0, -1, 0, -333, 3537]\) \(-40960/27\) \(-2700000000\) \([]\) \(720\) \(0.51063\) \(\Gamma_0(N)\)-optimal
1200.f1 1200l2 \([0, -1, 0, -30333, 2043537]\) \(-30866268160/3\) \(-300000000\) \([]\) \(2160\) \(1.0599\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1200.2.a.l

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 Cremona 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 Cremona labels.