Properties

Label 308550js
Number of curves 22
Conductor 308550308550
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("js1")
 
E.isogeny_class()
 

Elliptic curves in class 308550js

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.js2 308550js1 [1,0,0,42287,8873083][1, 0, 0, 42287, -8873083] 302111711/1404540302111711/1404540 38878566983437500-38878566983437500 [2][2] 27648002764800 1.86561.8656 Γ0(N)\Gamma_0(N)-optimal
308550.js1 308550js2 [1,0,0,471963,111208833][1, 0, 0, -471963, -111208833] 420021471169/50191650420021471169/50191650 13893370260257812501389337026025781250 [2][2] 55296005529600 2.21222.2122  

Rank

sage: E.rank()
 

The elliptic curves in class 308550js have rank 00.

Complex multiplication

The elliptic curves in class 308550js do not have complex multiplication.

Modular form 308550.2.a.js

sage: E.q_eigenform(10)
 
q+q2+q3+q4+q6+2q7+q8+q9+q12+4q13+2q14+q16q17+q184q19+O(q20)q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} + q^{9} + q^{12} + 4 q^{13} + 2 q^{14} + q^{16} - q^{17} + q^{18} - 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.