Properties

Label 2960.j
Number of curves $3$
Conductor $2960$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2960.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2960.j1 2960j1 \([0, -1, 0, -856, -9360]\) \(-16954786009/370\) \(-1515520\) \([]\) \(864\) \(0.30193\) \(\Gamma_0(N)\)-optimal
2960.j2 2960j2 \([0, -1, 0, -296, -21904]\) \(-702595369/50653000\) \(-207474688000\) \([]\) \(2592\) \(0.85124\)  
2960.j3 2960j3 \([0, -1, 0, 2664, 589040]\) \(510273943271/37000000000\) \(-151552000000000\) \([]\) \(7776\) \(1.4005\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2960.j have rank \(1\).

Complex multiplication

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

Modular form 2960.2.a.j

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} + q^{7} + q^{9} - 3 q^{11} - 4 q^{13} - 2 q^{15} + 3 q^{17} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.