Properties

Label 67760.s
Number of curves $2$
Conductor $67760$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 67760.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67760.s1 67760ch2 \([0, -1, 0, -97445, -11675783]\) \(-225637236736/1715\) \(-777786141440\) \([]\) \(194400\) \(1.4565\)  
67760.s2 67760ch1 \([0, -1, 0, -645, -30743]\) \(-65536/875\) \(-396829664000\) \([]\) \(64800\) \(0.90719\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 67760.s have rank \(1\).

Complex multiplication

The elliptic curves in class 67760.s do not have complex multiplication.

Modular form 67760.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.