Properties

Label 42978l
Number of curves 11
Conductor 4297842978
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 42978l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42978.j1 42978l1 [1,1,1,1276667,2378603125][1, 1, 1, 1276667, -2378603125] 230121178137769364003375/2578414527172744445952230121178137769364003375/2578414527172744445952 2578414527172744445952-2578414527172744445952 [][] 19420801942080 2.78942.7894 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42978l1 has rank 11.

Complex multiplication

The elliptic curves in class 42978l do not have complex multiplication.

Modular form 42978.2.a.l

sage: E.q_eigenform(10)
 
q+q2q3+q4q62q7+q8+q9+q11q12+q132q14+q163q17+q18+q19+O(q20)q + q^{2} - q^{3} + q^{4} - q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{11} - q^{12} + q^{13} - 2 q^{14} + q^{16} - 3 q^{17} + q^{18} + q^{19} + O(q^{20}) Copy content Toggle raw display