Properties

Label 17787j
Number of curves $1$
Conductor $17787$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 17787j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17787.ba1 17787j1 \([0, -1, 1, -1673954, -325258627]\) \(495616/243\) \(254340479262635251101\) \([]\) \(1182720\) \(2.6087\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 17787j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 17787j do not have complex multiplication.

Modular form 17787.2.a.j

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} + 3 q^{5} - 2 q^{6} + q^{9} + 6 q^{10} - 2 q^{12} - 4 q^{13} - 3 q^{15} - 4 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display