Properties

Label 46200dd
Number of curves $2$
Conductor $46200$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46200dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46200.cp2 46200dd1 \([0, 1, 0, -148, 608]\) \(11279504/693\) \(22176000\) \([2]\) \(9216\) \(0.16142\) \(\Gamma_0(N)\)-optimal
46200.cp1 46200dd2 \([0, 1, 0, -448, -2992]\) \(77860436/17787\) \(2276736000\) \([2]\) \(18432\) \(0.50799\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46200dd have rank \(1\).

Complex multiplication

The elliptic curves in class 46200dd do not have complex multiplication.

Modular form 46200.2.a.dd

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + q^{11} + 4 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.