Properties

Label 1320.k
Number of curves $2$
Conductor $1320$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1320.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1320.k1 1320d2 \([0, 1, 0, -1716, 17424]\) \(2184181167184/717482205\) \(183675444480\) \([2]\) \(1536\) \(0.86438\)  
1320.k2 1320d1 \([0, 1, 0, 309, 2034]\) \(203269830656/218317275\) \(-3493076400\) \([2]\) \(768\) \(0.51781\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1320.k have rank \(1\).

Complex multiplication

The elliptic curves in class 1320.k do not have complex multiplication.

Modular form 1320.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2 q^{7} + q^{9} + q^{11} - q^{15} - 8 q^{17} - 8 q^{19} + O(q^{20})\)  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.