Properties

Label 2960.m
Number of curves $4$
Conductor $2960$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2960.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2960.m1 2960n3 \([0, -1, 0, -84400, 9465792]\) \(16232905099479601/4052240\) \(16597975040\) \([2]\) \(6912\) \(1.3367\)  
2960.m2 2960n4 \([0, -1, 0, -84080, 9540800]\) \(-16048965315233521/256572640900\) \(-1050921537126400\) \([2]\) \(13824\) \(1.6832\)  
2960.m3 2960n1 \([0, -1, 0, -1200, 9152]\) \(46694890801/18944000\) \(77594624000\) \([2]\) \(2304\) \(0.78735\) \(\Gamma_0(N)\)-optimal
2960.m4 2960n2 \([0, -1, 0, 3920, 62400]\) \(1625964918479/1369000000\) \(-5607424000000\) \([2]\) \(4608\) \(1.1339\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2960.m have rank \(0\).

Complex multiplication

The elliptic curves in class 2960.m do not have complex multiplication.

Modular form 2960.2.a.m

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{5} - 2q^{7} + q^{9} + 2q^{13} + 2q^{15} + 6q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.