Properties

Label 2646l
Number of curves $3$
Conductor $2646$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2646l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2646.f2 2646l1 \([1, -1, 0, -597, -7043]\) \(-7414875/2744\) \(-8716379112\) \([]\) \(1728\) \(0.61753\) \(\Gamma_0(N)\)-optimal
2646.f1 2646l2 \([1, -1, 0, -52047, -4557281]\) \(-545407363875/14\) \(-400241898\) \([]\) \(5184\) \(1.1668\)  
2646.f3 2646l3 \([1, -1, 0, 4548, 71504]\) \(4492125/3584\) \(-8299415996928\) \([]\) \(5184\) \(1.1668\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2646l have rank \(1\).

Complex multiplication

The elliptic curves in class 2646l do not have complex multiplication.

Modular form 2646.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} - 5 q^{13} + q^{16} + 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.