Properties

Label 216.a
Number of curves $1$
Conductor $216$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 216.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216.a1 216a1 \([0, 0, 0, -12, 20]\) \(-3072\) \(-62208\) \([]\) \(24\) \(-0.36760\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 216.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 216.a do not have complex multiplication.

Modular form 216.2.a.a

sage: E.q_eigenform(10)
 
\(q - 4 q^{5} - 3 q^{7} - 4 q^{11} + q^{13} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display