Properties

Label 380.a
Number of curves 22
Conductor 380380
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 380.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
380.a1 380a2 [0,0,0,103,402][0, 0, 0, -103, -402] 472058064/475472058064/475 121600121600 [2][2] 4848 0.10516-0.10516  
380.a2 380a1 [0,0,0,8,3][0, 0, 0, -8, -3] 3538944/18053538944/1805 2888028880 [2][2] 2424 0.45173-0.45173 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 380.a have rank 11.

Complex multiplication

The elliptic curves in class 380.a do not have complex multiplication.

Modular form 380.2.a.a

sage: E.q_eigenform(10)
 
qq52q73q94q114q13+6q17+q19+O(q20)q - q^{5} - 2 q^{7} - 3 q^{9} - 4 q^{11} - 4 q^{13} + 6 q^{17} + 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.