Properties

Label 216384.ed
Number of curves $1$
Conductor $216384$
CM no
Rank $1$

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Show commands for: SageMath
sage: E = EllipticCurve("ed1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 216384.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.ed1 216384eh1 \([0, -1, 0, 28524991, 39341471457]\) \(83228502970940543/69854999176704\) \(-2154396594507624977793024\) \([]\) \(36495360\) \(3.3568\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 216384.ed1 has rank \(1\).

Complex multiplication

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

Modular form 216384.2.a.ed

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3q^{5} + q^{9} + 4q^{11} - 3q^{13} - 3q^{15} + 4q^{17} + O(q^{20})\)  Toggle raw display