Properties

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

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Show commands: SageMath
E = EllipticCurve("fz1")
 
E.isogeny_class()
 

Elliptic curves in class 232050.fz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
232050.fz1 232050fz1 [1,0,0,223497563387,24050365678645183][1, 0, 0, 223497563387, -24050365678645183] 1975431947052366089861272646117398175/15429943691048412952182418801950721975431947052366089861272646117398175/1542994369104841295218241880195072 964371480690525809511401175121920000-964371480690525809511401175121920000 [][] 45756057604575605760 5.59275.5927 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 232050.fz1 has rank 11.

Complex multiplication

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

Modular form 232050.2.a.fz

sage: E.q_eigenform(10)
 
q+q2+q3+q4+q6q7+q8+q94q11+q12+q13q14+q16q17+q18+q19+O(q20)q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - 4 q^{11} + q^{12} + q^{13} - q^{14} + q^{16} - q^{17} + q^{18} + q^{19} + O(q^{20}) Copy content Toggle raw display