Properties

Label 3120k
Number of curves $4$
Conductor $3120$
CM no
Rank $0$
Graph

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

Elliptic curves in class 3120k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.s4 3120k1 \([0, 1, 0, -20, -132]\) \(-3631696/24375\) \(-6240000\) \([2]\) \(768\) \(-0.012768\) \(\Gamma_0(N)\)-optimal
3120.s3 3120k2 \([0, 1, 0, -520, -4732]\) \(15214885924/38025\) \(38937600\) \([2, 2]\) \(1536\) \(0.33381\)  
3120.s1 3120k3 \([0, 1, 0, -8320, -294892]\) \(31103978031362/195\) \(399360\) \([2]\) \(3072\) \(0.68038\)  
3120.s2 3120k4 \([0, 1, 0, -720, -972]\) \(20183398562/11567205\) \(23689635840\) \([4]\) \(3072\) \(0.68038\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3120k have rank \(0\).

Complex multiplication

The elliptic curves in class 3120k do not have complex multiplication.

Modular form 3120.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 4q^{7} + q^{9} - 4q^{11} + q^{13} + q^{15} + 6q^{17} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.