Properties

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

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Show commands: SageMath
E = EllipticCurve("ii1")
 
E.isogeny_class()
 

Elliptic curves in class 216384ii

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.de1 216384ii1 \([0, -1, 0, -6785, -1875327]\) \(-2689684081/117006336\) \(-1502952938274816\) \([]\) \(718848\) \(1.5923\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 216384ii1 has rank \(1\).

Complex multiplication

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

Modular form 216384.2.a.ii

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