Properties

Label 786.g
Number of curves $1$
Conductor $786$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 786.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
786.g1 786h1 \([1, 0, 1, -17, 56]\) \(-498677257/1145988\) \(-1145988\) \([]\) \(168\) \(-0.14892\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 786.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 786.g do not have complex multiplication.

Modular form 786.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} - 2 q^{7} - q^{8} + q^{9} + 2 q^{10} + 3 q^{11} + q^{12} - 5 q^{13} + 2 q^{14} - 2 q^{15} + q^{16} + 7 q^{17} - q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display