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Properties

Label 6552e
Number of curves $2$
Conductor $6552$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 6552e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6552.b1 6552e1 \([0, 0, 0, -87, -310]\) \(10536048/91\) \(628992\) \([2]\) \(1792\) \(-0.062964\) \(\Gamma_0(N)\)-optimal
6552.b2 6552e2 \([0, 0, 0, -27, -730]\) \(-78732/8281\) \(-228953088\) \([2]\) \(3584\) \(0.28361\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6552e have rank \(1\).

Complex multiplication

The elliptic curves in class 6552e do not have complex multiplication.

Modular form 6552.2.a.e

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} + q^{7} + 4 q^{11} + q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.