Properties

Label 277335e
Number of curves $1$
Conductor $277335$
CM no
Rank $1$

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

Elliptic curves in class 277335e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277335.e1 277335e1 \([0, 0, 1, -147, -855]\) \(-481890304/154075\) \(-112320675\) \([]\) \(194304\) \(0.25763\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 277335e1 has rank \(1\).

Complex multiplication

The elliptic curves in class 277335e do not have complex multiplication.

Modular form 277335.2.a.e

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