Properties

Label 281775c
Number of curves $1$
Conductor $281775$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 281775c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
281775.c1 281775c1 \([0, -1, 1, -253838, 120536588]\) \(-10372034560/29937843\) \(-5220978276868494075\) \([]\) \(10340352\) \(2.2786\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 281775c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 281775c do not have complex multiplication.

Modular form 281775.2.a.c

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