Properties

Label 3960.s
Number of curves 22
Conductor 39603960
CM no
Rank 00
Graph

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

Elliptic curves in class 3960.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3960.s1 3960a1 [0,0,0,267,1674][0, 0, 0, -267, -1674] 76136652/27576136652/275 76032007603200 [2][2] 12801280 0.181450.18145 Γ0(N)\Gamma_0(N)-optimal
3960.s2 3960a2 [0,0,0,147,3186][0, 0, 0, -147, -3186] 6353046/75625-6353046/75625 4181760000-4181760000 [2][2] 25602560 0.528020.52802  

Rank

sage: E.rank()
 

The elliptic curves in class 3960.s have rank 00.

Complex multiplication

The elliptic curves in class 3960.s do not have complex multiplication.

Modular form 3960.2.a.s

sage: E.q_eigenform(10)
 
q+q5+4q7q114q132q176q19+O(q20)q + q^{5} + 4 q^{7} - q^{11} - 4 q^{13} - 2 q^{17} - 6 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the LMFDB numbering.

(1221)\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.