Properties

Label 15210w
Number of curves 22
Conductor 1521015210
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 15210w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.q2 15210w1 [1,1,0,64674,6725120][1, -1, 0, -64674, -6725120] 3869893/300-3869893/300 2319204012875100-2319204012875100 [2][2] 9984099840 1.69591.6959 Γ0(N)\Gamma_0(N)-optimal
15210.q1 15210w2 [1,1,0,1053324,415828490][1, -1, 0, -1053324, -415828490] 16718302693/9016718302693/90 695761203862530695761203862530 [2][2] 199680199680 2.04252.0425  

Rank

sage: E.rank()
 

The elliptic curves in class 15210w have rank 00.

Complex multiplication

The elliptic curves in class 15210w do not have complex multiplication.

Modular form 15210.2.a.w

sage: E.q_eigenform(10)
 
qq2+q4+q5q8q104q11+q16+4q174q19+O(q20)q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4 q^{11} + q^{16} + 4 q^{17} - 4 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 Cremona 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 Cremona labels.