Properties

Label 575.e
Number of curves $1$
Conductor $575$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 575.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
575.e1 575c1 \([0, -1, 1, -458, 3943]\) \(-5451776/23\) \(-44921875\) \([]\) \(280\) \(0.32301\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 575.e1 has rank \(0\).

Complex multiplication

The elliptic curves in class 575.e do not have complex multiplication.

Modular form 575.2.a.e

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} + q^{7} + q^{9} + 4 q^{12} + 2 q^{13} + 2 q^{14} - 4 q^{16} - 5 q^{17} + 2 q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display