Properties

Label 1216.r
Number of curves $1$
Conductor $1216$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1216.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1216.r1 1216m1 \([0, 0, 0, 20, -16]\) \(27000/19\) \(-622592\) \([]\) \(192\) \(-0.19970\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1216.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1216.r do not have complex multiplication.

Modular form 1216.2.a.r

sage: E.q_eigenform(10)
 
\(q + 3 q^{3} + q^{7} + 6 q^{9} + 2 q^{11} + q^{13} + 3 q^{17} - q^{19} + O(q^{20})\)  Toggle raw display