Properties

Label 232050.ef
Number of curves 11
Conductor 232050232050
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("ef1")
 
E.isogeny_class()
 

Elliptic curves in class 232050.ef

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
232050.ef1 232050ef1 [1,1,1,300138,863891031][1, 1, 1, -300138, 863891031] 7654674371496385/821165814155232-7654674371496385/821165814155232 320767896154387500000-320767896154387500000 [][] 92160009216000 2.61432.6143 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 232050.ef1 has rank 11.

Complex multiplication

The elliptic curves in class 232050.ef do not have complex multiplication.

Modular form 232050.2.a.ef

sage: E.q_eigenform(10)
 
q+q2q3+q4q6q7+q8+q9q11q12q13q14+q16q17+q18+3q19+O(q20)q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} - q^{11} - q^{12} - q^{13} - q^{14} + q^{16} - q^{17} + q^{18} + 3 q^{19} + O(q^{20}) Copy content Toggle raw display