Properties

Label 603.e
Number of curves $1$
Conductor $603$
CM no
Rank $1$

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

Elliptic curves in class 603.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
603.e1 603e1 \([1, -1, 0, -9, -54]\) \(-117649/1809\) \(-1318761\) \([]\) \(96\) \(-0.14429\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 603.e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 603.e do not have complex multiplication.

Modular form 603.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} - 5 q^{7} - 3 q^{8} + q^{10} + 4 q^{11} - 4 q^{13} - 5 q^{14} - q^{16} - 6 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display