Properties

Label 1452d
Number of curves $2$
Conductor $1452$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 1452d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1452.f2 1452d1 \([0, 1, 0, 323, 1340]\) \(131072/99\) \(-2806152624\) \([2]\) \(720\) \(0.50108\) \(\Gamma_0(N)\)-optimal
1452.f1 1452d2 \([0, 1, 0, -1492, 10052]\) \(810448/363\) \(164627620608\) \([2]\) \(1440\) \(0.84765\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1452d have rank \(0\).

Complex multiplication

The elliptic curves in class 1452d do not have complex multiplication.

Modular form 1452.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} + 2 q^{7} + q^{9} + 2 q^{13} + 2 q^{15} - 4 q^{17} + 6 q^{19} + O(q^{20})\) Copy content 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.