Properties

Label 6760.i
Number of curves $4$
Conductor $6760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6760.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6760.i1 6760g3 \([0, 0, 0, -18083, -935922]\) \(132304644/5\) \(24713262080\) \([2]\) \(9216\) \(1.0803\)  
6760.i2 6760g2 \([0, 0, 0, -1183, -13182]\) \(148176/25\) \(30891577600\) \([2, 2]\) \(4608\) \(0.73369\)  
6760.i3 6760g1 \([0, 0, 0, -338, 2197]\) \(55296/5\) \(386144720\) \([2]\) \(2304\) \(0.38711\) \(\Gamma_0(N)\)-optimal
6760.i4 6760g4 \([0, 0, 0, 2197, -74698]\) \(237276/625\) \(-3089157760000\) \([2]\) \(9216\) \(1.0803\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6760.i have rank \(0\).

Complex multiplication

The elliptic curves in class 6760.i do not have complex multiplication.

Modular form 6760.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.