Properties

Label 277350r
Number of curves $1$
Conductor $277350$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 277350r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277350.r1 277350r1 \([1, 1, 0, -2575, -50375]\) \(523181/12\) \(43335937500\) \([]\) \(282240\) \(0.82741\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 277350r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 277350r do not have complex multiplication.

Modular form 277350.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 3 q^{11} - q^{12} + 2 q^{13} - q^{14} + q^{16} + 2 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display