Properties

Label 31478b
Number of curves 11
Conductor 3147831478
CM no
Rank 33

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 31478b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31478.a1 31478b1 [1,0,1,5,12][1, 0, 1, -5, 12] 10218313/62956-10218313/62956 62956-62956 [][] 55365536 0.39551-0.39551 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 31478b1 has rank 33.

Complex multiplication

The elliptic curves in class 31478b do not have complex multiplication.

Modular form 31478.2.a.b

sage: E.q_eigenform(10)
 
qq22q3+q43q5+2q64q7q8+q9+3q102q112q12q13+4q14+6q15+q166q17q184q19+O(q20)q - q^{2} - 2 q^{3} + q^{4} - 3 q^{5} + 2 q^{6} - 4 q^{7} - q^{8} + q^{9} + 3 q^{10} - 2 q^{11} - 2 q^{12} - q^{13} + 4 q^{14} + 6 q^{15} + q^{16} - 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20}) Copy content Toggle raw display