Properties

Label 56784ba
Number of curves $1$
Conductor $56784$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 56784ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56784.bv1 56784ba1 \([0, 1, 0, -320272, 77958596]\) \(-20994006260678308/3063651608241\) \(-530183292715754496\) \([]\) \(921600\) \(2.1313\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 56784ba1 has rank \(1\).

Complex multiplication

The elliptic curves in class 56784ba do not have complex multiplication.

Modular form 56784.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{3} - 3 q^{5} + q^{7} + q^{9} - 3 q^{15} + 7 q^{17} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display