Properties

Label 3120.q
Number of curves $4$
Conductor $3120$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3120.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3120.q1 3120u3 \([0, 1, 0, -7736, 259284]\) \(12501706118329/2570490\) \(10528727040\) \([2]\) \(3072\) \(0.92018\)  
3120.q2 3120u2 \([0, 1, 0, -536, 2964]\) \(4165509529/1368900\) \(5607014400\) \([2, 2]\) \(1536\) \(0.57361\)  
3120.q3 3120u1 \([0, 1, 0, -216, -1260]\) \(273359449/9360\) \(38338560\) \([2]\) \(768\) \(0.22703\) \(\Gamma_0(N)\)-optimal
3120.q4 3120u4 \([0, 1, 0, 1544, 22100]\) \(99317171591/106616250\) \(-436700160000\) \([2]\) \(3072\) \(0.92018\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3120.q have rank \(1\).

Complex multiplication

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

Modular form 3120.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} - q^{13} - q^{15} - 6q^{17} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.