Properties

Label 1617.f
Number of curves $2$
Conductor $1617$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 1617.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1617.f1 1617d2 \([1, 1, 0, -3560, 49029]\) \(14553591673375/5208653241\) \(1786568061663\) \([2]\) \(2560\) \(1.0518\)  
1617.f2 1617d1 \([1, 1, 0, 675, 5832]\) \(98931640625/96059601\) \(-32948443143\) \([2]\) \(1280\) \(0.70523\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1617.f have rank \(0\).

Complex multiplication

The elliptic curves in class 1617.f do not have complex multiplication.

Modular form 1617.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - 3 q^{8} + q^{9} - q^{11} + q^{12} + 4 q^{13} - q^{16} - 4 q^{17} + q^{18} + 8 q^{19} + O(q^{20})\) 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 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.