Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1216.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1216.p1 1216g1 \([0, -1, 0, -5, 29]\) \(-1024/19\) \(-311296\) \([]\) \(128\) \(-0.26491\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1216.p1 has rank \(0\).

Complex multiplication

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

Modular form 1216.2.a.p

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + q^{5} - 3 q^{7} + q^{9} + 3 q^{11} + 4 q^{13} + 2 q^{15} + 5 q^{17} + q^{19} + O(q^{20})\)  Toggle raw display