Properties

Label 5775ba
Number of curves $1$
Conductor $5775$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 5775ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5775.c1 5775ba1 \([0, 1, 1, -308, -1906]\) \(5186867200/754677\) \(471673125\) \([]\) \(4032\) \(0.38944\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5775ba1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5775ba do not have complex multiplication.

Modular form 5775.2.a.ba

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} + q^{7} + q^{9} + q^{11} + 2 q^{12} + 3 q^{13} - 2 q^{14} - 4 q^{16} - q^{17} - 2 q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display