Properties

Label 2760.c
Number of curves $2$
Conductor $2760$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2760.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2760.c1 2760b2 \([0, -1, 0, -856, 9100]\) \(33909572018/3234375\) \(6624000000\) \([2]\) \(2688\) \(0.62231\)  
2760.c2 2760b1 \([0, -1, 0, 64, 636]\) \(27871484/198375\) \(-203136000\) \([2]\) \(1344\) \(0.27573\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2760.c have rank \(0\).

Complex multiplication

The elliptic curves in class 2760.c do not have complex multiplication.

Modular form 2760.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 4 q^{7} + q^{9} - 6 q^{11} - 4 q^{13} + q^{15} + 2 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.