Properties

Label 57330eq
Number of curves $1$
Conductor $57330$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("eq1")
 
E.isogeny_class()
 

Elliptic curves in class 57330eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57330.eh1 57330eq1 \([1, -1, 1, -2931557, -11868329469]\) \(-662989657192009/14097531093750\) \(-59245437321803417343750\) \([]\) \(7526400\) \(3.0505\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 57330eq1 has rank \(0\).

Complex multiplication

The elliptic curves in class 57330eq do not have complex multiplication.

Modular form 57330.2.a.eq

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - 4 q^{11} - q^{13} + q^{16} - 5 q^{17} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display