Properties

Label 42135i
Number of curves 11
Conductor 4213542135
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 42135i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42135.i1 42135i1 [0,1,1,525265,145678306][0, 1, 1, -525265, 145678306] 5705690236075638784/302672257031255705690236075638784/30267225703125 8502063700007812585020637000078125 [][] 653184653184 2.09312.0931 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 42135i1 has rank 11.

Complex multiplication

The elliptic curves in class 42135i do not have complex multiplication.

Modular form 42135.2.a.i

sage: E.q_eigenform(10)
 
q+q32q4+q5+4q7+q94q112q12+q15+4q16+2q17+7q19+O(q20)q + q^{3} - 2 q^{4} + q^{5} + 4 q^{7} + q^{9} - 4 q^{11} - 2 q^{12} + q^{15} + 4 q^{16} + 2 q^{17} + 7 q^{19} + O(q^{20}) Copy content Toggle raw display