Properties

Label 75810z
Number of curves $1$
Conductor $75810$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 75810z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75810.p1 75810z1 \([1, 1, 0, -672, 8064]\) \(-93182366881/29393280\) \(-10610974080\) \([]\) \(104832\) \(0.63692\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 75810z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 75810z do not have complex multiplication.

Modular form 75810.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 6 q^{11} - q^{12} - 6 q^{13} + q^{14} - q^{15} + q^{16} - 3 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display