Properties

Label 209088.fr
Number of curves 11
Conductor 209088209088
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("fr1")
 
E.isogeny_class()
 

Elliptic curves in class 209088.fr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
209088.fr1 209088dh1 [0,0,0,6534,215622][0, 0, 0, -6534, -215622] 13824-13824 2231656650432-2231656650432 [][] 311040311040 1.11911.1191 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 209088.fr1 has rank 11.

Complex multiplication

The elliptic curves in class 209088.fr do not have complex multiplication.

Modular form 209088.2.a.fr

sage: E.q_eigenform(10)
 
q+2q53q73q132q173q19+O(q20)q + 2 q^{5} - 3 q^{7} - 3 q^{13} - 2 q^{17} - 3 q^{19} + O(q^{20}) Copy content Toggle raw display