Properties

Label 74529.f
Number of curves $1$
Conductor $74529$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 74529.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
74529.f1 74529be1 \([1, -1, 1, 30388, -8184900]\) \(17999471/177957\) \(-30683069090337573\) \([]\) \(774144\) \(1.8447\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 74529.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 74529.f do not have complex multiplication.

Modular form 74529.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 4 q^{5} + 3 q^{8} + 4 q^{10} - 5 q^{11} - q^{16} + 3 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display