Properties

Label 4200.j
Number of curves $2$
Conductor $4200$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4200.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4200.j1 4200h1 \([0, -1, 0, -28, 52]\) \(78608/21\) \(672000\) \([2]\) \(512\) \(-0.17350\) \(\Gamma_0(N)\)-optimal
4200.j2 4200h2 \([0, -1, 0, 72, 252]\) \(318028/441\) \(-56448000\) \([2]\) \(1024\) \(0.17307\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4200.j have rank \(1\).

Complex multiplication

The elliptic curves in class 4200.j do not have complex multiplication.

Modular form 4200.2.a.j

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.