Properties

Label 462f
Number of curves 44
Conductor 462462
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 462f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.g4 462f1 [1,0,0,97,1337][1, 0, 0, -97, 1337] 100999381393/723148272-100999381393/723148272 723148272-723148272 [4][4] 192192 0.383080.38308 Γ0(N)\Gamma_0(N)-optimal
462.g3 462f2 [1,0,0,2517,48285][1, 0, 0, -2517, 48285] 1763535241378513/46123113961763535241378513/4612311396 46123113964612311396 [2,2][2, 2] 384384 0.729660.72966  
462.g2 462f3 [1,0,0,3507,6507][1, 0, 0, -3507, 6507] 4770223741048753/27405748657984770223741048753/2740574865798 27405748657982740574865798 [2][2] 768768 1.07621.0762  
462.g1 462f4 [1,0,0,40247,3104415][1, 0, 0, -40247, 3104415] 7209828390823479793/495093067209828390823479793/49509306 4950930649509306 [2][2] 768768 1.07621.0762  

Rank

sage: E.rank()
 

The elliptic curves in class 462f have rank 00.

Complex multiplication

The elliptic curves in class 462f do not have complex multiplication.

Modular form 462.2.a.f

sage: E.q_eigenform(10)
 
q+q2+q3+q4+2q5+q6q7+q8+q9+2q10+q11+q122q13q14+2q15+q162q17+q18+O(q20)q + q^{2} + q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + 2 q^{10} + q^{11} + q^{12} - 2 q^{13} - q^{14} + 2 q^{15} + q^{16} - 2 q^{17} + q^{18} + 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.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with Cremona labels.