Properties

Label 6762.p
Number of curves $2$
Conductor $6762$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 6762.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.p1 6762s1 \([1, 0, 1, -105180, -12121574]\) \(3188856056959/274710528\) \(11085560685674496\) \([2]\) \(75264\) \(1.8197\) \(\Gamma_0(N)\)-optimal
6762.p2 6762s2 \([1, 0, 1, 114340, -56025574]\) \(4096768048001/35984932992\) \(-1452121843880502144\) \([2]\) \(150528\) \(2.1663\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6762.p have rank \(0\).

Complex multiplication

The elliptic curves in class 6762.p do not have complex multiplication.

Modular form 6762.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} - q^{8} + q^{9} - 2 q^{10} - 6 q^{11} + q^{12} - 6 q^{13} + 2 q^{15} + q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.