Properties

Label 76664.k
Number of curves $2$
Conductor $76664$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76664.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76664.k1 76664k2 \([0, -1, 0, -55216, -4915572]\) \(3543122/49\) \(257475776595968\) \([2]\) \(405504\) \(1.5708\)  
76664.k2 76664k1 \([0, -1, 0, -456, -206212]\) \(-4/7\) \(-18391126899712\) \([2]\) \(202752\) \(1.2242\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 76664.k have rank \(1\).

Complex multiplication

The elliptic curves in class 76664.k do not have complex multiplication.

Modular form 76664.2.a.k

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + 4q^{5} + q^{7} + q^{9} + 8q^{15} + 2q^{17} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.