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Properties

Label 1014.f
Number of curves $2$
Conductor $1014$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1014.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1014.f1 1014f1 \([1, 0, 0, -62, 324]\) \(-156116857/186624\) \(-31539456\) \([]\) \(384\) \(0.13273\) \(\Gamma_0(N)\)-optimal
1014.f2 1014f2 \([1, 0, 0, 523, -6111]\) \(93603087383/150994944\) \(-25518145536\) \([]\) \(1152\) \(0.68203\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1014.f have rank \(1\).

Complex multiplication

The elliptic curves in class 1014.f do not have complex multiplication.

Modular form 1014.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 3 q^{5} + q^{6} - 2 q^{7} + q^{8} + q^{9} - 3 q^{10} - 6 q^{11} + q^{12} - 2 q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.