Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1216.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1216.j1 1216a1 \([0, 0, 0, -2, 2]\) \(-13824/19\) \(-1216\) \([]\) \(32\) \(-0.71557\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1216.j1 has rank \(1\).

Complex multiplication

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

Modular form 1216.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 3q^{9} - 3q^{11} + 4q^{13} - 3q^{17} - q^{19} + O(q^{20})\)  Toggle raw display