Properties

Label 216384hd
Number of curves $1$
Conductor $216384$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("hd1")
 
E.isogeny_class()
 

Elliptic curves in class 216384hd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.m1 216384hd1 \([0, -1, 0, -2172, 80046]\) \(-3072832/5589\) \(-2062046258496\) \([]\) \(430080\) \(1.0530\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 216384hd1 has rank \(0\).

Complex multiplication

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

Modular form 216384.2.a.hd

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