Properties

Label 216384hc
Number of curves $1$
Conductor $216384$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("hc1")
 
E.isogeny_class()
 

Elliptic curves in class 216384hc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.p1 216384hc1 \([0, -1, 0, -1857, 31809]\) \(-110328386/1587\) \(-10192551936\) \([]\) \(190464\) \(0.72527\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 216384hc1 has rank \(1\).

Complex multiplication

The elliptic curves in class 216384hc do not have complex multiplication.

Modular form 216384.2.a.hc

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